Projective Modules Research Articles

On generalized Nakayama–Azumaya’s lemma

In the recent publication, generalized Nakayama–Azumaya’s lemma, i.e. Azumaya’s lemma (or Nakayama’s lemma) extended to a module which is isomorphic to a direct summand of a direct sum of finitely generated modules, is conjectured to hold. A proof of this conjecture is the main objective of the present paper. It is achieved by proving the nonexistence of non-zero weak Nakayama–Azumaya special modules, and showing that the canonical map is a non-split epimorphism if Mi is finitely generated and for each As an application of generalized Nakayama–Azumaya’s lemma, we show the existence of maximal submodules for some classes of modules. This implies, in particular, Bass’ result concerning the class of projective modules.

Homological theory of k-idempotent ideals in dualizing varieties

In this work, we develop the theory of k-idempotent ideals in the setting of dualizing varieties. Several results given previously by Auslander et al. are extended to this context. Given an ideal (which is the trace of a projective module), we construct a canonical recollement which is the analog to a well-known recollement in categories of modules over artin algebras. Moreover, we study the homological properties of the categories involved in such a recollement. Consequently, we find conditions on the ideal to obtain quasi-hereditary algebras in such a recollement. Applications to bounded derived categories are also given.

Congruences for critical values of higher derivatives of twisted Hasse–Weil L-functions, III

AbstractLetAbe an abelian variety defined over a number fieldk, letpbe an odd prime number and let$F/k$be a cyclic extension ofp-power degree. Under not-too-stringent hypotheses we give an interpretation of thep-component of the relevant case of the equivariant Tamagawa number conjecture in terms of integral congruence relations involving the evaluation on appropriate points ofAof the${\rm Gal}(F/k)$-valued height pairing of Mazur and Tate. We then discuss the numerical computation of this pairing, and in particular obtain the first numerical verifications of this conjecture in situations in which thep-completion of the Mordell–Weil group ofAoverFis not a projective Galois module.

Model structures, recollements and duality pairs

In this paper, we construct some model structures corresponding Gorenstein [Formula: see text]-modules and relative Gorenstein flat modules associated to duality pairs, Frobenius pairs and cotorsion pairs. By investigating homological properties of Gorenstein [Formula: see text]-modules and some known complete hereditary cotorsion pairs, we describe several types of complexes and obtain some characterizations of Iwanaga–Gorenstein rings. Based on some facts given in this paper, we find new duality pairs and show that [Formula: see text] is covering as well as enveloping and [Formula: see text] is preenveloping under certain conditions, where [Formula: see text] denotes the class of Gorenstein [Formula: see text]-injective modules and [Formula: see text] denotes the class of Gorenstein [Formula: see text]-flat modules. We give some recollements via projective cotorsion pair [Formula: see text] cogenerated by a set, where [Formula: see text] denotes the class of Gorenstein [Formula: see text]-projective modules. Also, many recollements are immediately displayed through setting specific complete duality pairs.

On relative counterpart of Auslander’s conditions

It is now well known that the conditions used by Auslander to define the Gorenstein projective modules on Noetherian rings are independent. Recently, Ringel and Zhang adopted a new approach in investigating Auslander’s conditions. Instead of looking for examples, they investigated rings on which certain implications between Auslander’s conditions hold. In this paper, we investigate the relative counterpart of Auslander’s conditions. So, we extend Ringel and Zhang’s work and introduce other concepts. Namely, for a semidualizing module [Formula: see text], we introduce weakly [Formula: see text]-Gorenstein and partially [Formula: see text]-Gorenstein rings as rings representing relations between the relative counterpart of Auslander’s conditions. Moreover, we introduce a relative notion of the well-known Frobenius category. We show how useful are [Formula: see text]-Frobenius categories in characterizing weakly [Formula: see text]-Gorenstein and partially [Formula: see text]-Gorenstein rings.

Some Results on Pure Ideals and Trace Ideals of Projective Modules

Let R be a commutative ring with the unit element. It is shown that an ideal I in R is pure if and only if Ann(f) + I = R for all f ∈ I. If J is the trace of a projective R-module M, we prove that J is generated by the “coordinates” of M and JM = M. These lead to a few new results and alternative proofs for some known results.

On the primefulness of local cohomology modules

Let be a commutative Noetherian ring with identity For a non-zero module . We prove that a multiplication primeful module and are I-cofinite and primeful, for each where is an ideal of with . As a consequence, we deduce that, if and are multiplication primeful R- modules, then is primeful. Another result is, for a projective module over an integral domain, admits projective resolution such that each is primeful (faithfully flat).

Direct Projective Modules, Direct Injective Modules, and their Generalizations

This paper contains new and previously known results on modules that are close to direct projective and direct injective modules. The main results are presented with proofs.

ABOUT THE PROGRAM OF THE STAFF OF THE URFU STUDENT TEAMS ON THE FORMATION OF FUTURE SKILLS

The article emphasizes the importance of the skills of the future in the training of a modern specialist in the labor market. A list of relevant skills of the future is given. A research design is presented in the development of a program for the formation of the skills of the future in the environment of student teams. The article analyzes the scientific literature on the topic of this study, describes the portrait of a soldier of the student detachments of UrFU in the context of the skills of the future. Conclusions are made about the skills of the future that are in demand by the fighters of student teams. Technologies for the formation of the skills of the future in the environment of student teams are proposed. The article presents a program for the formation of the skills of the future among the student teams of the Ural Federal University. The program consists of 4 modules: an information module, which includes 4 lectures from the speakers of the UPI, Ural State University-Ural Federal University Alumni Association and the Ural Federal University's Center of Universal Competencies "4K", an interactive module consisting of four trainings, a project module including "Creative Laboratory". The practical module contains five activities aimed at building the skills of the future. The results of testing some of the elements of the program for the formation of skills in the environment of student teams are presented. The conclusion is made about the significant potential of the movement of student teams in the formation of the skills of the future.

Characterizations of Weakly Approximately Primary Submodules in Some Types of Modules

Our aim in this note is to introduce several characterizations of weakly approximately primary submodules in class of multiplication modules. Furthermore, we characterized weakly approximately primary submodules by theirs resudule in the class of multiplication modules with the help of some types of modules as non-singular, projective, regular and faithful modules. Also, we characterized weakly approximately primary ideal with some kind of weakly approximately primary submodules in the same previous classes of modules with help of finitely generated modules.

Analysis and Stabilization of Slopes Using Geo5 Software

Abstract: With the development of technology and software, it has become easy to solve difficult problems in every field which use to take a lot of time. The use of software in the field of civil engineering has grown since the last decade. GEO5 is one such software which may be used to solve many geotechnical problems. GEO5 consists of wide range of powerful programs based on analytical method sand the Finite Element Method such as Stability Analysis, Excavation Design, Retaining, Wall Design, Foundation Design, Soil Settlement Analysis, Digital Terrain Model, Geotechnical Finite Element Analysis like analyzing and design of slope, design of retaining walls, settlement analysis, foundation design and much more .It is a very simple and powerful tool for solving geotechnical problems based on traditional analytical methods and Finite Element Methods (FEM).The easy-to-use suite consists of individual programs with a unified and user-friendly interface. Each program is used to analyze a different geotechnical task but all modules communicate with each other to form an integrated suite. In this project modules related to slope stability have been studied in details and then used them for analysis of slope stability. Using GEO5 software the geometry of problems were created in GEO5 and the analysis were carried out considering the stability and economic considerations. Also, the costs of different types of reinforcing methods were determined and compared. It is found that soil nailing is most economical. Keywords: GEO5software, Analysis, Soil nailing, Anti-slide Piles, Anchors, Reinforcemet

Minimizing transportation cost of prefabricated modules in modular construction projects

PurposeThe objective of this research study is to formulate and develop a novel optimization model that enables planners of modular construction to minimize the total transportation and storage costs of prefabricated modules in modular construction projects.Design/methodology/approachThe model is developed by identifying relevant decision variables, formulating an objective function capable of minimizing the total transportation and storage costs and modelling relevant constraints. The model is implemented by providing all relevant planner-specified data and performing the model optimization computations using mixed-integer programming to generate the optimal solution.FindingsA case study of hybrid modular construction of a healthcare facility is used to evaluate the model performance and demonstrate its capabilities in minimizing the total transportation and onsite storage costs of building prefabricated modules.Research limitations/implicationsThe model can be most effective in optimizing transportation for prefabricated modules with rectangular shapes and might be less effective for modules with irregular shapes. Further research is needed to consider the shape of onsite storage area and its module arrangement.Practical implicationsThe developed model supports construction planners in improving the cost effectiveness of modular construction projects by optimizing the transportation of prefabricated modules from factories to construction sites.Originality/valueThe original contributions of this research is selecting an optimal module truck assignment from a feasible set of trucks, identifying an optimal delivery day of each module as well as its location and orientation on the assigned truck and complying with relevant constraints including the non-overlap of modules on each truck, shipment weight distribution and aerodynamic drag reduction.

Levi-Civita connections for a class of noncommutative minimal surfaces

In this paper, we study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e. finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus for such modules, and provide a characterization in terms of the existence of a pseudo-inverse of the matrix representing the hermitian form with respect to a set of generators. As a first illustration of the above concepts, we find metric connections on the fuzzy sphere. Finally, the framework is applied to a class of noncommutative minimal surfaces, for which there is a natural concept of torsion, and we prove that there exist metric and torsion free connections for every minimal surface in this class.

C-PURE SUBMODULES AND C-FLAT MODULES

Let R be a ring. A right R-module A is said to be C-flat if the kernel of any epimorphism B → A is C-pure in B, i.e. the induced map Hom(C,B) → Hom(C,A) is surjective for any cyclic right R-module C. Projective modules are C-flat and C-flat modules are weakly-flat and neat-flat. In this article, it is discussed the connections between C-flat, weakly-flat, neat-flat and singly flat modules. It is shown that C-flat modules coincide with singly-projective modules over arbitrary rings. Next, several characterizations of certain classes of rings and modules via C-purity are considered. We prove that, every C-flat module is injective if and only if R is a QF ring. Moreover, we show that R is a CF ring if and only if every FP-injective right R-module is C-flat.

Two-term tilting complexes for preprojective algebras of non-Dynkin type

In this paper, we study two-term tilting complexes for preprojective algebras of non-Dynkin type. We show that there exist two families of two-term tilting complexes, which are respectively parameterized by the elements of the corresponding Coxeter group. Moreover, we provide the complete classification in the case of affine type by showing that any two-term silting complex belongs one of them. For this purpose, we also discuss the Krull–Schmidt property for the homotopy category of finitely generated projective modules over a complete ring.

The road from ICPD to SDGs: Health returns of reducing the unmet need for family planning in India

ObjectiveThis study attempts to estimate the impact of reducing the unmet need for family planning on the key maternal and child health indicators in India from 1993 to 2016, and projecting this for the period from 2016 to 2030. Data and methodsThe data have been compiled from various sources such as the United Nations’ World Population prospects, national family health surveys and the sample registration system. The family planning and demographic projection modules of ‘Spectrum’, a modular computer simulation program, were used to estimate the impact of family planning programmes on reproductive, maternal and child health outcomes in India from 1993 to 2030. ResultsReduction of the unmet need for family planning averted approximately 56 million unintended pregnancies, 7 million unsafe abortions and 167,000 maternal deaths between 1993 and 2016. It is expected that an additional 41 million unintended pregnancies, 5 million unsafe abortions and 124,000 maternal deaths can be avoided by reducing the unmet need for family planning to 5% by 2030. Similarly, the declining unmet need for family planning between 1993 and 2016 led to a reduction in the pregnancy rate, abortion rate, and risk-adjusted infant and under-five mortality rates by 27 per 1000 married women, 1.8 per million married women, 10 per 1000 live births and 15 per 1000 live births, respectively. It is expected that approximately 24 pregnancies per 1000 married women, 1.6 abortions per million married women, 10 risk adjusted infant deaths per 1000 live births, and 14 under-five deaths per 1000 live births can be avoided by reducing the unmet need for family planning to 5% by 2030. ConclusionsThe findings of this study advocate that family planning is one of the best return on-investment strategies for India to achieve several targets under the reproductive, maternal and child health-related sustainable development goals.

An end-to-end network for segmenting the vasculature of three retinal capillary plexuses from OCT angiographic volumes.

The segmentation of en face retinal capillary angiograms from volumetric optical coherence tomographic angiography (OCTA) usually relies on retinal layer segmentation, which is time-consuming and error-prone. In this study, we developed a deep-learning-based method to segment vessels in the superficial vascular plexus (SVP), intermediate capillary plexus (ICP), and deep capillary plexus (DCP) directly from volumetric OCTA data. The method contains a three-dimensional convolutional neural network (CNN) for extracting distinct retinal layers, a custom projection module to generate three vascular plexuses from OCTA data, and three parallel CNNs to segment vasculature. Experimental results on OCTA data from rat eyes demonstrated the feasibility of the proposed method. This end-to-end network has the potential to simplify OCTA data processing on retinal vasculature segmentation. The main contribution of this study is that we propose a custom projection module to connect retinal layer segmentation and vasculature segmentation modules and automatically convert data from three to two dimensions, thus establishing an end-to-end method to segment three retinal capillary plexuses from volumetric OCTA without any human intervention.

Characterizations of right rejective chains

AbstractIn this paper, we give characterizations of the category of finitely generated projective modules having a right rejective chain. By focusing on the characterizations, we give sufficient conditions for right rejective chains to be total right rejective chains. Moreover, we prove that Nakayama algebras with heredity ideals, locally hereditary algebras and algebras of global dimension at most two satisfy the sufficient conditions. As an application, we show that these algebras are right-strongly quasi-hereditary algebras.

Relative (pre)-modular categories from special linear Lie superalgebras

We examine two different m-traces in the category of representations over the quantum Lie superalgebra associated to sl(m|n) at root of unity. The first m-trace is on the ideal of projective modules and leads to new Extended Topological Quantum Field Theories. The second m-trace is on the ideal of perturbative typical modules. We consider the quotient with respect to negligible morphisms coming from this m-trace and show that in the case of sl(2|1) this quotient leads to 3-manifolds invariants. We conjecture that the quotient category of perturbatives over quantum sl(m|n) leads to 3-manifold invariants and more generally ETQFTs.

Unmanned aerial vehicles supporting imagery intelligence using the structured light technology

One of the possible tasks for unmanned aerial vehicles (UAVs) is field capturing of object images. The field capturing of object images (scenes) is possible owing to the UAV equipped with photographic cameras, TV cameras, infrared camer-as or synthetic aperture radars (SAR). The result of the recognition is a metric mapping of space, i.e. 2D flat images. In order to increase the quality of image recognition, it is necessary to search for and develop stereoscopic visualization with the possibility of its mobile use. A pioneering approach presented in the research paper is using a UAV with an imagery intelligence system based on structured light technology for air reconnaissance of object over a selected area or in a given direction in the field. The outcome of imagery intelligence is a three-dimensional (3D imaging) information on the geometry of an observed scene. The visualization with a stereoscopic interface proposed in the work allows for a natural perception of the depth of the scene and mutual spatial relationships, as well as seeing which objects are closer and which are further. The essence of the article is to present the application of three-dimensional vision measurement technology on UAVs. The paper presents an analysis of the possibilities of using UAVs for image recognition and a method of image recognition based on the technology of structural lighting using the method of projection of Gray’a fringes and codes. The designed image recognition system based on the structural lighting technology is described. It also discusses task modules forming a measuring head, i.e., projection, detection and calculation modules, and the exchange of control or measurement data between imaging system components. It presents the results of tests on the possibility of rapidly acquiring images using a UAV. The test results and the analyses indicate that using a UAV with an imaging technology based on structural light can contribute to improving the abilities to detect, identify, locate and monitor objects at close range, within a selected direction outdoors or indoors.