Class Of Rings Research Articles

Characterizations of maximal z°-ideals of C(X) and real maximal ideals of q(X)

In this paper we first give elementwise characterizations of real maximal ideals and maximal z°-ideals of C(X). Next, using this we characterize the real maximal ideals of the classical ring of quotients q(X) of C(X) and also maximal z°-ideals of factor rings of C(X). We show that every real maximal ideal of q(X) is precisely the extension of a real maximal ideal of C(X) which is also a z° -ideal, i.e., the extension of Mp for some almost P -point p of υX. Using this fact it turns out that in contrast to C(X), q(X) may not contain any real maximal ideal. We observe that every maximal ideal of q(X) is real if and only if X is a pseudocompact almost P -space, i.e., q(X) = C*(X). We also observe that the real maximal ideals of q(X) are precisely the extensions of the real maximal ideals of C(X) when and only when X is an almost P -space, i.e., q(X) = C(X).

Quasi-clean rings and strongly quasi-clean rings

An element [Formula: see text] of a ring [Formula: see text] is called a quasi-idempotent if [Formula: see text] for some central unit [Formula: see text] of [Formula: see text], or equivalently, [Formula: see text], where [Formula: see text] is a central unit and [Formula: see text] is an idempotent of [Formula: see text]. A ring [Formula: see text] is called a quasi-Boolean ring if every element of [Formula: see text] is quasi-idempotent. A ring [Formula: see text] is called (strongly) quasi-clean if each of its elements is a sum of a quasi-idempotent and a unit (that commute). These rings are shown to be a natural generalization of the clean rings and strongly clean rings. An extensive study of (strongly) quasi-clean rings is conducted. The abundant examples of (strongly) quasi-clean rings state that the class of (strongly) quasi-clean rings is very larger than the class of (strongly) clean rings. We prove that an indecomposable commutative semilocal ring is quasi-clean if and only if it is local or [Formula: see text] has no image isomorphic to [Formula: see text]; For an indecomposable commutative semilocal ring [Formula: see text] with at least two maximal ideals, [Formula: see text]([Formula: see text]) is strongly quasi-clean if and only if [Formula: see text] is quasi-clean if and only if [Formula: see text], [Formula: see text] is a maximal ideal of [Formula: see text]. For a prime [Formula: see text] and a positive integer [Formula: see text], [Formula: see text] is strongly quasi-clean if and only if [Formula: see text]. Some open questions are also posed.

Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations.

Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, “A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function,” J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-νNAC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl–carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600–3600 cm−1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-νNAC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.

Revisiting the Partial Ring Current Model: Longitudinal Asymmetry of Ground Magnetic Depression During Geomagnetic Storms

AbstractDuring the main phase of geomagnetic storms, the horizontal ground magnetic component is more depressed at dusk than at dawn, which was originally explained by the partial ring current model. Later studies questioned the idea that the ring current intensifies primarily at dusk, and the cause of this dawn‐dusk asymmetry still remains to be understood. The present study targets this old issue by statistically examining SuperMAG geomagnetic (sub‐)indices. The results are summarized as follows: (1) the dawn‐dusk asymmetry is correlated with the enhancement of the dawnside westward auroral electrojet (AEJ); (2) its correlation with the duskside eastward AEJ, which was considered by the classical partial ring current model, is insignificant; (3) the magnetic depression tends to be larger on the dayside than on the nightside, and the asymmetry is correlated with the westward AEJ in the midnight sector; (4) the dawn‐dusk asymmetry enhances typically for 1–2 h, and the day‐night asymmetry for <1 h; (5) the dawn‐dusk and day‐night asymmetries are not correlated with each other. It is suggested that the dawn‐dusk asymmetry is associated with a dawnside wedge current system with an enhanced westward AEJ (1 & 2), and it is suggested to be driven by a substorm‐like process, and possibly also by enhanced global convection (4). The day‐night asymmetry is probably associated with the formation of the substorm wedge current system (3 & 4). Although the associated dawnside and midnight westward AEJs may often enhance simultaneously, they are possibly driven by different processes (4 & 5).

An Innovative Method for Microcapsule Based Functional Yarn Production

ABSTRACT Today, microcapsule application to textile materials is a widely used for the production of functional textile products. Microcapsule application methods used in practice have some significant disadvantages. There is a need for innovative methods to eliminate or minimize these disadvantages. From this point of view, in this study, it was aimed to develop an alternative method based on integrating microcapsule particles into the open staple fiber bundle before the spun yarn formation on the classical ring spinning. It was thought that this application method could allow the incorporating microcapsules not only the fibers on the yarn surface but also to the surface of the fibers in the yarn structure. Microcapsule doped and undoped ring spun yarns having Ne 16 yarn count with knitted twist were produced from viscose fibers. Obtained ring spun yarns were subjected to winding and knitting processes in order to analyze the effect of friction on the microcapsule presence. SEM images taken from yarn and fabric samples were examined. Additionally, yarn properties were analyzed. In order to evaluate the performance of the alternative method, microcapsule dispersion at the same concentration was applied to the knitted fabrics using pad-dry-cure method, which was widely used for production of the functional textile products. Two types of microcapsule applied knitted fabric samples were washed several times and presence of microcapsules was evaluated with SEM images. Furthermore, thermal properties of the both types of application methods were compared by examining T-history curves. The findings indicated that the alternative method offers comparable yarn and thermal properties with environmentally friendly application as well as washable and durable to the friction effects occurring in industrial processes.

On strongly coseparable modules

A module M is called mathfrak {s}-coseparable if for every nonzero submodule U of M such that M/U is finitely generated, there exists a nonzero direct summand V of M such that V subseteq U and M/V is finitely generated. It is shown that every non-finitely generated free module is mathfrak {s}-coseparable but a finitely generated free module is not, in general, mathfrak {s}-coseparable. We prove that the class of mathfrak {s}-coseparable modules over a right noetherian ring is closed under finite direct sums. We show that the class of commutative rings R for which every cyclic R-module is mathfrak {s}-coseparable is exactly that of von Neumann regular rings. Some examples of modules M for which every direct summand of M is mathfrak {s}-coseparable are provided.

Semicommutative involution rings

In this paper, we establish a generalization of the class of semicommutative rings which is called * -semicommutative ring. We also discuss the relations among * -semicommutative rings, * -reversible rings and reversible rings. Moreover, we investigate some properties of these rings.

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.

Parametrizing torsion pairs in derived categories

We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) of a ring A A . To this end, we provide a construction of t-structures from chains in the lattice of ring epimorphisms starting in A A , which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. We also provide constructions of silting and cosilting objects in D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) . This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.

On Borromean links and related structures.

The creation of knotted, woven and linked molecular structures is an exciting and growing field in synthetic chemistry. Presented here is a description of an extended family of structures related to the classical `Borromean rings', in which no two rings are directly linked. These structures may serve as templates for the designed synthesis of Borromean polycatenanes. Links of n components in which no two are directly linked are termed `n-Borromean' [Liang & Mislow (1994). J. Math. Chem. 16, 27-35]. In the classic Borromean rings the components are three rings (closed loops). More generally, they may be a finite number of periodic objects such as graphs (nets), or sets of strings related by translations as in periodic chain mail. It has been shown [Chamberland & Herman (2015). Math. Intelligencer, 37, 20-25] that the linking patterns can be described by complete directed graphs (known as tournaments) and those up to 13 vertices that are vertex-transitive are enumerated. In turn, these lead to ring-transitive (isonemal) n-Borromean rings. Optimal piecewise-linear embeddings of such structures are given in their highest-symmetry point groups. In particular, isonemal embeddings with rotoinversion symmetry are described for three, five, six, seven, nine, ten, 11, 13 and 14 rings. Piecewise-linear embeddings are also given of isonemal 1- and 2-periodic polycatenanes (chains and chain mail) in their highest-symmetry setting. Also the linking of n-Borromean sets of interleaved honeycomb nets is described.

Abstract Algebra

Ring hypothesis is one of the pieces of the theoretical polynomial math that has been thoroughly used in pictures. Nevertheless, ring hypothesis has not been associated with picture division. In this paper, we propose another rundown of similarity among pictures using rings and the entropy work. This new record was associated as another stopping standard to the Mean Shift Iterative Calculation with the goal to accomplish a predominant division. An examination on the execution of the calculation with this new ending standard is finished. In spite of the fact that ring hypothesis and class hypothesis from the start sought after assorted direction it turned out during the 1970s – that the investigation of functor groupings furthermore reveals new plots for module hypothesis.

N-chained semigroups and -perspective modules and rings

We introduce and study a new class of modules and rings we call -perspective, which can either be described in terms of perspective direct summands, associate idempotents, or generalized inverses. When n is small (), we recover existing class of modules and rings: (endo)abelian, strongly IC, and perspective ones. And 3/2-perspective rings are characterized by all their regular elements being special clean. Standard constructions are also discussed and examples are provided.

Study of Von Neumann Abelian Regular Rings

This paper is concerned with the basic properties of a class of regular rings of some "classical" type. Abelian regular rings are, however, a more indirect concept, in that a nontrivial theorem is required to show that strongly regular rings are actually regular. For this reason, we view abelianness as the more natural property. We first collect a number of equivalent characterizations of abelian regular rings, before proving that "abelian regular" is equivalent to "strongly regular".
 GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 14-20

Some remarks on Nonnil-coherent rings and ϕ-IF rings

Let [Formula: see text] be a commutative ring. If the nilpotent radical [Formula: see text] of [Formula: see text] is a divided prime ideal, then [Formula: see text] is called a [Formula: see text]-ring. In this paper, we first distinguish the classes of nonnil-coherent rings and [Formula: see text]-coherent rings introduced by Bacem and Ali [Nonnil-coherent rings, Beitr. Algebra Geom. 57(2) (2016) 297–305], and then characterize nonnil-coherent rings in terms of [Formula: see text]-flat modules, nonnil-injective modules and nonnil-FP-injective modules. A [Formula: see text]-ring [Formula: see text] is called a [Formula: see text]-IF ring if any nonnil-injective module is [Formula: see text]-flat. We obtain some module-theoretic characterizations of [Formula: see text]-IF rings. Two examples are given to distinguish [Formula: see text]-IF rings and IF [Formula: see text]-rings.

On the integral domains characterized by a Bezout property on intersections of principal ideals

In this article we study two classes of integral domains. The first is characterized by having a finite intersection of principal ideals being finitely generated only when it is principal. The second class consists of the integral domains in which a finite intersection of principal ideals is always non-finitely generated except in the case of containment of one of the principal ideals in all the others. We relate these classes to many well-studied classes of integral domains, to star operations and to classical and new ring constructions.

On the Grothendieck–Serre conjecture on principal bundles in mixed characteristic

Let $R$ be a regular local ring. Let $\mathbf {G}$ be a reductive $R$-group scheme. A conjecture of Grothendieck and Serre predicts that a principal ${\mathbf {G}}$-bundle over $R$ is trivial if it is trivial over the quotient field of $R$. The conjecture is known when $R$ contains a field. We prove the conjecture for a large class of regular local rings

High-resolution spectral analysis of long single-frequency pulses generated by a self-sweeping Yb-doped fiber laser

Continuous wave self-sweeping operation is demonstrated in a classical ring cavity configuration of Yb-doped fiber laser with a saturable absorber, which is usually used to obtain single-frequency lasing. Using heterodyne-based high-resolution spectral analysis we demonstrate that the laser generates a series of long (up to 1 ms) rectangular pulses consisting of single frequency radiation (the linewidth <0.7 MHz). At the same time, the lasing frequency changes between pulses regularly in a stepwise manner by one intermode beating frequency within a self-sweeping range of 100 pm. The effect of cavity configuration on pulse parameters (duration and chirp) is investigated. We also demonstrate that saturable absorbing mirrors design can be used to control the self-sweeping direction and value of the frequency jump.

On strongly dccr⋆ modules

In this paper, we introduce and study the concept of strongly dccr[Formula: see text] modules. Strongly dccr[Formula: see text] condition generalizes the class of Artinian modules and it is stronger than dccr[Formula: see text] condition. Let [Formula: see text] be a commutative ring with nonzero identity and [Formula: see text] a unital [Formula: see text]-module. A module [Formula: see text] is said to be strongly [Formula: see text] if for every submodule [Formula: see text] of [Formula: see text] and every sequence of elements [Formula: see text] of [Formula: see text], the descending chain of submodules [Formula: see text] of [Formula: see text] is stationary. We give many examples and properties of strongly dccr[Formula: see text]. Moreover, we characterize strongly dccr[Formula: see text] in terms of some known class of rings and modules, for instance in perfect rings, strongly special modules and principally cogenerately modules. Finally, we give a version of Union Theorem and Nakayama’s Lemma in light of strongly dccr[Formula: see text] concept.

Square element graph of square-subtract rings

If [Formula: see text] is a ring then the square element graph [Formula: see text] is the simple undirected graph whose vertex set consists of all non-zero elements of [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text] for some [Formula: see text]. In this paper, we provide some necessary and sufficient conditions for the connectedness of [Formula: see text], where [Formula: see text] is a ring with identity. We mainly characterize some special class of ring [Formula: see text] which we call square-subtract ring for which the graph [Formula: see text] is connected.

A Study of Nil Ideals and Kothe’s Conjecture in Neutrosophic Rings

The aim of this study is to determine the necessary and sufficient condition for any AH subset to be a full ideal in a neutrosophic ring R(I) and to be a nil ideal too. Also, this work shows the equivalence between Kothe’s conjecture in classical rings and corresponding neutrosophic rings, i.e., it proves that Kothe’s conjecture is true in the neutrosophic ring R(I) if and only if it is true in the corresponding classical ring R.