Coherent Ring Research Articles

Dynamics of ultrafast magnetization reversal in submicron elliptical Permalloy thin film elements

The micromagnetic dynamics of ultrafast magnetization reversal in elliptical Permalloy $({\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20})$ thin film elements is described. It is shown that coherent rotation and magnetization ringing in submicron Py elements can be controlled by adjusting the axis ratio of the ellipse, the thickness, and the angle of the magnetic field pulse. For the elliptical Py element with $400\text{\ensuremath{-}}\mathrm{nm}$-long axis, $200\text{\ensuremath{-}}\mathrm{nm}$-short axis, and $4.7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thickness, the nonuniform distribution of magnetization results from a strong in-plane, nonuniform demagnetization field during magnetization precession. It is the main reason magnetization ringing appears, even though the average values of ${M}_{y}$ and ${M}_{z}$ are equal to zero at the moment the pulse is terminated. The simulation results indicate that uniformity in the distribution of the magnetization during reversal is improved by reducing the length of the short axis from $200\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}112\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, and reducing the thickness of the thin film from $4.7\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}3.2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The modification in the geometric configuration of the element is found to effectively suppress the magnetization ringing.

Extensions of Injectivity and Coherent Rings

ABSTRACT For a ring D and a subring C, let ℛ[D,C ] = {(d 1,…, d n , c,c,…): d i ∈ D, c ∈ C, n ≥ 1}, a subring of , and let , a subring of 𝕄2(D). In this article, various conditions are obtained for ℛ[D,C ] and D∝ D to be right (m,n)-injective (in particular, P-injective, f-injective, FP-injective), right coherent, and right FC. Right nonsingular right (m,n)-injective rings are characterized using their maximal right quotient rings. Communicated by I. Swanson.

The weak dimensions of Gaussian rings

We provide necessary and sufficient conditions for a Gaussian ring $R$ to be semihereditary, or more generally, of $w.dimR\leq 1$. Investigating the weak global dimension of a Gaussian coherent ring $R$, we show that the only values $w.dimR$ may take are $0,1$ and $\infty$; but that $fP.dimR$ is always at most one. In particular, we conclude that a Gaussian coherent ring $R$ is either Von Neumann regular, or semihereditary, or non-regular of $w.dimR=\infty$.

On (m,n)-Injective Modules and (m,n)-Coherent Rings

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m,n)-injective in case every right R-homomorphism from an n-generated submodule of Rm to M extends to one from Rm to M. R is said to be left (m,n)-coherent if each n-generated submodule of the left R-module Rm is finitely presented. In this paper, we give some new characterizations of (m,n)-injective modules. We also derive various equivalent conditions for a ring to be left (m,n)-coherent. Some known results on coherent rings are obtained as corollaries.

Rings Whose Modules Have Grade Zero

In this paper, we prove that R is a two-sided Artinian ring and J is a right annihilator ideal if and only if (i) for any nonzero right module, there is a nonzero linear map from it to a projective module; (ii) every submodule of RR is not a radical module for some right coherent rings. We call a ring a right X ring if HomR(M, R) = 0 for any right module M implies that M = 0. We can prove some left Goldie and right X rings are right Artinian rings. Moreover we characterize semisimple rings by using X rings. A famous Faith’s conjecture is whether a semipimary PF ring is a QF ring. Similarly we study the relationship between X rings and QF and get many interesting results.

The Canis Major dwarf galaxy as the progenitor of the Monoceros tidal stream

The Sloan Digital Sky Survey has recently discovered a coherent ring of stars at low galactic latitude that is believed to be the tidal stream of a merging dwarf galaxy in the Galactic plane (named the Monoceros tidal stream). The existence and location of the core of its progenitor galaxy is still controversial. The best candidate is the Canis Major dwarf galaxy, a distinct overdensity of red stars discovered in the 2MASS survey, but also interpreted as the signature of the Galactic warp viewed in projection. In this paper, we report a variety of new observational evidence that supports the notion that CMa is the remnant of a partially disrupted core of a dwarf satellite. The comparison of the orbit derived from our theoretical model for the parent galaxy of this ring-like structure with an accurate determination of CMa orbit leads to the conclusion that this satellite is the best candidate for the progenitor of the Monoceros tidal stream.

On Weakly Finite Conductor Rings#

We define a weakly finite conductor rings with zero divisors, and examine the transfer of these rings to the trivial ring extensions. These results provide examples of a weakly finite conductor rings that are not finite conductor rings (and so not coherent rings). The last section show that the class of weakly finite conductor rings and the class of 2-coherent rings are not comparable.

Théorie algorithmique des anneaux arithmétiques, des anneaux de Prüfer et des anneaux de Dedekind

We give a basic constructive theory for Prüfer rings and Dedekind rings. All results are given in a direct algorithmic way. Our proofs are often more simple and more general than the ones we found in classical literature. Many definitions have to be reformulated in an equivalent but constructive way. We do not assume in general to deal with domains, whence the importance given to arithmetical rings, Prüfer rings (arithmetical reduced rings) and Prüfer coherent rings (semi-hereditary rings). Our general setting for Dedekind rings does not include complete factorisation of invertible ideals. We prefer to use partial factorisation bases for finite families of invertible ideals, since they always do exist constructively. Moreover, many important results are obtained in the weaker setting of Prüfer coherent rings or of dimension one Prüfer coherent rings.

Tracer Leakage from Modeled Agulhas Rings

In a numerical, isopycnal, ocean model the mixing is investigated with the environment of two idealized Agulhas rings, one that splits, and one that remains coherent. The evolution of a passive tracer, initially contained within the rings, shows that tracer leakage is associated with the formation of filaments in the early stage of ring evolution. These filaments reach down to the thermocline. In the deepest layers leakage occurs on a larger scale. Self-advection of the rings is very irregular, and it is not possible to compute a Lagrangian boundary in order to estimate the transport of leakage from the rings. To describe the processes that govern tracer leakage, in a coordinate frame moving with the ring a kinematic separatrix is defined in the streamfunction field for the nondivergent flow. Initially, filaments arise because of the elongation of the ring, which is mainly governed by an m = 2 instability that is collaborating with differential rotation. Because of beta, the symmetry is destroyed related to the separatrix associated with a stagnation point in the flow. The filament upstream of the stagnation point grows much faster and is associated with the bulk of tracer leakage. Mixing is enhanced by time dependence of the separatrix. As a result, there are no large differences between the leakage from a coherent ring, where the m = 2 instability equilibrates, and from a splitting ring, where the m = 2 instability keeps growing, which confirms that the amount of leakage is mainly governed by the ring's initial deformation combined with unsteady self-advection of the ring and not by the splitting of the ring. The decay of tracer content in the thermocline shows that in the first months up to 40% of the ring water can be mixed with the environment. In deeper layers the decay of tracer content may reach up to 90%.

The existence of Gorenstein flat covers

We prove that all left modules over a right coherent ring have Gorenstein flat covers.

Self-persistent currents in coherent magnetic rings

It is shown that when a magnetic ring is cooled below its coherent temperature, with coherent length larger than the ring one, a perfectly measured non-negligible persistent current appears when the magnetization sets perpendicular to the plane of the ring, that is to say in the case of perpendicular magnetic anisotropy. This may happen in strained thin layer of magnetic metals and semiconductors. In particular, an application for a possible experiment in Ni thin films and Ni/Cu trilayers, showing perpendicular magnetic anisotropy, is discussed where magnetic fluxes of several quantum units can be reached that should lead to nA currents.

Hidden quantum pump effects in quantum coherent rings

Time periodic perturbations of an electron system on a ring are examined. For small frequencies, periodic small amplitude perturbations give rise to sideband currents which, in leading order, are inversely proportional to the frequency. These sideband currents compensate the current of the central band such that to leading order, no net pumped current is generated. In the nonadiabatic limit, larger pump frequencies can lead to resonant excitations: as a consequence, a net pumped current arises. We illustrate our results for a one-channel ring with a quantum dot whose barriers are modulated parametrically.

A study of synthetic jets from rectangular and dual-circular orifices

AbstractThe results of an investigation into the effect of both the number of orifices and the geometry of these orifices on the fluid structures exiting from a synthetic jet actuator are presented. The experiments have used smoke and laser visualisation and single hotwire measurement techniques to establish the flow field exiting the various orifices and the fluid velocities in the exit plane of the orifice. The results indicate that the use of two small orifices can perhaps produce two coherent vortex rings with a total circulation greater than that found in the ring produced by a large, single orifice of equivalent area. However, they have also shown that there are three different types of interaction between two adjacent orifices, related to the spacing between them and the level of excitation applied to the diaphragm. In addition, these interactions may affect the overall level of circulation in different ways. Finally the results have shown that a rectangular orifice of a given exit plane area is more likely to produce a turbulent ring than the equivalent circular orifice due to a ‘smoothing’ process which endeavours to create an axisymmetric ring from a non-axisymmetric slug of fluid. This work has shown that when using synthetic jet actuators in flow control applications, care should be taken in selecting the spacing and geometry of the orifices used, as certain set-ups may be more suited to certain applications than others.

Covers and Envelopes via Endoproperties of Modules

Let R be a ring and MR be an R-module. We characterize the existence of Add M-covers and Add M-envelopes in terms of finiteness conditions of M over its endomorphism ring. We then present some applications related to the existence of well-behaved direct sum decompositions for direct products of copies of M. Our results can be viewed as natural extensions of classical theorems of Bass and Chase on coherent and perfect rings. 2000 Mathematics Subject Classification 16D90, 16G10, 16S50, 16D40, 16P70, 16E50.

On t-Structures and Tilting Theory

Let A be a right coherent associative ring with unit. We introduce the notion of coendofinite complex and we associate to such a complex a t-structure in D b (mod A). We give conditions for the heart of that t-structure to be a module category. We also give some applications in connection with derived equivalent rings and tilting theory. In particular for a tilting module over a finite dimensional k-algebra, we get a reformulation of Brenner-Butler's theorem in terms of t-structures.

Homological Characterizations of Rings with Property (P)

A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and Π-coherent rings with property (P).

ON MODULES WHICH ARE SUBISOMORPHIC TO THEIR PURE-INJECTIVE ENVELOPES

In the present paper, modules which are subisomorphic (in the sense of Goldie) to their pure-injective envelopes are studied. These modules will be called almost pure-injective modules. It is shown that every module is isomorphic to a direct summand of an almost pure-injective module. We prove that these modules are ker-injective (in the sense of Birkenmeier) over pure-embeddings. For a coherent ring R, the class of almost pure-injective modules coincides with the class of ker-injective modules if and only if R is regular. Generally, the class of almost pure-injective modules is neither closed under direct sums nor under elementary equivalence. On the other hand, it is closed under direct products and if the ring has pure global dimension less than or equal to one, it is closed under reduced products. Finally, pure-semisimple rings are characterized, in terms of almost pure-injective modules.

COHERENCE

ABSTRACT The theory of coherent rings and modules is generalized to cardinal numbers . A ring R is -coherent if every right ideal with less than -generators has less than -relations.

WHEN ARE PURE-INJECTIVE ENVELOPES OF FLAT MODULES FLAT?

ABSTRACT The question is answered in terms of flat covers, flat cotorsion modules, and cotorsion envelopes. It is shown that the corresponding class of rings properly contains that of coherent rings. The perfect rings among those are given a ring-theoretic description.

On f -injective modules

In this paper, the notions of f-injective and f*-injective modules are introduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutely pure. We prove that the class \( \Sigma^* \) of f*-injective modules is closed under ultraproducts. On the other hand, \( \Sigma^* \) is not axiomatisable. For coherent rings R, \( \Sigma^* \) is axiomatisable iff every \( \chi_0 \)-injective module is f*-injective. Further, it is shown that the class \( \Sigma \) of f-injective modules is axiomatisable iff R is coherent and every \( \chi_0 \)-injective module is f-injective. Finally, an f-injective module H, such that every module embeds in an ultraprower of H, is given.