In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...

We give a different proof for a structure theorem of Hausser and Nill on Hopf modules over quasi-Hopf algebras. We extend the structure theorem to a classification of two-sided two-cosided Hopf modules by YetterDrinfeld modules, which can be defined in two rather different manners for the quasi-Hopf case. The category equivalence between Hopf modules and Yetter-Drinfeld modules leads to a new c...

let $alpha$ be an automorphism of a ring $r$. the authors [on skewinverse laurent-serieswise armendariz rings, comm. algebra 40(1)(2012) 138-156] applied the concept of armendariz rings to inverseskew laurent series rings and introduced skew inverselaurent-serieswise armendariz rings. in this article, we study on aspecial type of these rings and introduce strongly armendariz ringsof inverse ske...

We define a 0-Hecke action on composition tableaux, and then use it to derive 0-Hecke modules whose quasisymmetric characteristic is a quasisymmetric Schur function. We then relate the modules to the weak Bruhat order and use them to derive a new basis for quasisymmetric functions. We also classify those modules that are tableau-cyclic and likewise indecomposable. Finally, we develop a restrict...

Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse ske...

In this paper, using generalized partial skew versions of Armendariz rings, we study the transfer of left (right) zip property between a ring R and partial skew generalized power series rings

Recommended by Francois Goichot In this article, we study the relationship between left right zip property of R and skew polynomial extension over R, using the skew versions of Armendariz rings.