The first two papers of this series1 were primarily concerned with a closure operation on the lattice of right ideals of a ring and the resulting direct-sum representation of the ring in case the closure operation was atomic. These results generalize the classical structure theory of semisimple rings. The present paper studies the irreducible components encountered in the direct-sum representat...

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

We define the presented dimensions for modules and rings to measure how far away a module is from having an infinite finite presentation and develop ways to compute the projective dimension of a module with a finite presented dimension and the right global dimension of a ring. We also make a comparison of the right global dimension, the weak global dimension, and the presented dimension and div...

For a left and right Noetherian ring $R$, we give some equivalent characterizations for $\_RR$ satisfying the Auslander condition in terms of flat (resp. injective) dimensions minimal injective coresolution resolution) $R$-modules. Furthermore, prove that an artin algebra $R$ condition, is Gorenstein if only subcategory consisting finitely generated modules contravariantly finite. As applicatio...

MAXIMAL QUOTIENT RINGS AND ESSENTIAL RIGHT IDEALS IN GROUP RINGS OF LOCALLY FINITE GROUPS Theorem . zero . FERRAN CEDÓ * AND BRIAN HARTLEY Dedicated to the memory of Pere Menal Let k be a commutative field . Let G be a locally finite group without elements of order p in case char k = p > 0 . In this paper it is proved that the type I. part of the maximal right quotient ring of the group algebgr...

It is well known that the set of all ideals(2) of a ring forms a complete modular lattice with respect to set inclusion. The same is true of the set of all right ideals. Our purpose in this paper is to consider the consequences of imposing certain additional restrictions on these ideal lattices. In particular, we discuss the case in which one or both of these lattices is complemented, and the c...

The family of rings the form
 \frac{\mathbb{Z}_{4}\left \langle x,y \right \rangle}{\left x^2-a,y^2-b,yx-xy-2(c+dx+ey+fxy) \rangle}
 is investigated which contains generalized Hamilton quaternions over $\Z_4$. These are local order 256. This has 256 contained in 88 distinct isomorphism classes. Of non-isomorphic rings, 10 minimal reversible nonsymmetric and 21 abelian reflexive nonsem...

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...

We have previously demonstrated that pulmonary vasodilation in response to isoproterenol is attenuated in conscious dogs after left lung autotransplantation (LLA). Our present goal was to identify the cellular mechanism responsible for this dysfunction. Size- and position-matched pulmonary arterial rings were isolated from the right (control) and left (LLA) lungs of 23 dogs 1-14 mo post-LLA. Th...

In this paper, we present a switch based on coupling and resonance in thegraphene plate and rings operating at 10 THz. This structure consists of several layers ofHexagonal Boron Nitride (hBN), SiO2 and P+Si, such that graphene plates and rings areinside the hBN layer. The terahertz wave is incident from the upper part of the switchand Surface Plasmons (SPs) are excited ...