Modules which are epi-equivalent to projective modules
Modules which are invariant under idempotents of their envelopes
We study the class of modules which are invariant under idempotents of their envelopes. We say that a module M is -idempotent-invariant if there exists an -envelope u : M → X such that for any idempotent g ∈ End(X) there exists an endomorphism f : M → M such that uf = gu. The properties of this class of modules are discussed. We prove that M is -idempotent-invariant if and only if for every decomposition , we have . Moreover, some generalizations of -idempotent-invariant modules are considered....
Modules with semiregular endomorphism rings
We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.
Modules with the direct summand sum property
The present work gives some characterizations of -modules with the direct summand sum property (in short DSSP), that is of those -modules for which the sum of any two direct summands, so the submodule generated by their union, is a direct summand, too. General results and results concerning certain classes of -modules (injective or projective) with this property, over several rings, are presented.
Moduln, die in jeder Erweiterung ein Komplement haben.
Monoidal categories for Morita theory
More on matrix near-rings.
More on Morita contexts for near-rings.
More on the Schur group of a commutative ring.
Morita duality for Grothendieck categories.
We survey some recent results on the theory of Morita duality for Grothendieck categories, comparing two different versions of this concept, and giving applications to QF-3 and Qf-3' rings.
Morita equivalence for regular algebras
Morita Equivalences of Functor Categories and Decompositions of Functors Defined on a Category Associated to Algebras with One-Side Units
Conditions which imply Morita equivalences of functor categories are described. As an application a Dold-Kan type theorem for functors defined on a category associated to associative algebras with one-side units is proved.
Morita-injektive Moduln über kommutativen Dedekind-Ringen.
Morphisms and modules for poly-bicategories.
Multi-bimodels
*-multilinear polynomials with invertible values
-flat and -FP-injective modules
In this paper, we study the existence of the -flat preenvelope and the -FP-injective cover. We also characterize -coherent rings in terms of the -FP-injective and -flat modules.
--coherent rings and Gorenstein graded modules
Let be a graded ring and be an integer. We introduce and study the notions of Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules by using the notion of special finitely presented graded modules. On -gr-coherent rings, we investigate the relationships between Gorenstein -FP-gr-injective and Gorenstein -gr-flat modules. Among other results, we prove that any graded module in -gr (or gr-) admits a Gorenstein -FP-gr-injective (or Gorenstein -gr-flat) cover and preenvelope, respectively....
Natural dualities between abelian categories
In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them.
Near-rings in which each prime factor is simple.