Let R be a discrete valuation ring with a unique maximal ideal πR and a quotient field K, and let F = R/πR be the residue class field. Let n ≥ 2 be an integer and {λij | 1 ≤ i, j ≤ n} a set of n integers satisfying λii = 0, λik + λkj ≥ λij , λij + λji > 0 (if i = j) for all 1 ≤ i, j, k ≤ n. Then Λ = (πijR) is a basic semiperfect Noetherian R-subalgebra of the full n× n matrix algebra Mn(K). We ...

w x In 8 , K. Morita introduced a useful notion of duality between categories of modules, usually called ‘‘Morita duality.’’ He proved that every duality is given by contravariant hom functors defined by a bimodule which is an injective cogenerator for both categories of modules. On the other hand, the equivalences between categories of comodules over a coalgebra w x were characterized by M. Ta...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

We introduce a theory of modules over representation small category taking values in entwining structures semiperfect coalgebra. This takes forward the aim developing categories entwined to same extent as that module well philosophy Mitchell working with rings several objects. The representations are motivated by work Estrada and Virili, who developed preadditive categories, which were then stu...

in this paper $s$ is a monoid with a left zero and $a_s$ (or $a$) is a unitary right $s$-act. it is shown that a monoid $s$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $s$-act is quasi-projective. also it is shown that if every right $s$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...