Quasi-invertibility Monoform Modules

Invertibility of Multiplication Modules

Invertibility of multiplication modules All rings are commutative with 1 and all modules are unital. Let R be a ring and M an R-module. M is called multiplication if for each submodule N of M, N=IM for some ideal I of R. Multiplication modules have recently received considerable attention during the last twenty years. In this talk we give the de nition of invertible submodules as a natural gene...

On quasi-catenary modules

We call a module M , quasi-catenary if for each pair of quasi-prime submodules K and L of M with K L all saturated chains of quasi-prime submodules of M from K to L have a common finite length. We show that any homomorphic image of a quasi-catenary module is quasi-catenary. We prove that if M   is a module with following properties: (i) Every quasi-prime submodule of M has finite quasi-height;...

On quasi-baer modules

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

On δ-Quasi Armendariz Modules

Quasi-Exact Sequence and Finitely Presented Modules

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.