A General Injectivity for Modules.
A Generalisation of Swan's Theorem.
A generalization of a theorem of Faith and Menal and applications.
A generalization of Mathieu subspaces to modules of associative algebras
We first propose a generalization of the notion of Mathieu subspaces of associative algebras , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to -modules . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable...
A generalization of reflexive rings
We introduce a class of rings which is a generalization of reflexive rings and -reversible rings. Let be a ring with identity and denote the Jacobson radical of . A ring is called -reflexive if for any , implies . We give some characterizations of a -reflexive ring. We prove that some results of reflexive rings can be extended to -reflexive rings for this general setting. We conclude some relations between -reflexive rings and some related rings. We investigate some extensions of...
A generalization of the prime radical of an ideal.
A generalization of Ulm subgroups
A generalized Picard group for prime rings
A graph associated to proper non-small ideals of a commutative ring
In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring , denoted by , is a graph with all non-small proper ideals of as vertices and two distinct vertices and are adjacent if and only if is not small in . In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter,...
A Homological Finiteness Criterion.
A Krull-Schmidt theorem for Artinian modules over local rings.
A Morita equivalence for Hilbert C*-modules
We introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate the properties of the new Morita equivalence. We apply our results to study continuous actions of locally compact groups on full Hilbert C*-modules. We also present an extension of Green's theorem in the context of Hilbert C*-modules.
A Morita type theorem for a sort of quotient categories
We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.
A noncommutative generalization of Auslander's last theorem.
A non-commutative minimally non-Noetherian ring.
A note on block triangular presentations of rings and finitistic dimension
A note on -cofinitely supplemented modules.
A note on -modules.
A note on finitely generated ideal-simple commutative semirings
Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.
A note on flat modules