in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...

Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion $S$-prime submodule which is generalization prime used them to characterize certain classes rings/modules such as submodules, simple modules, torsion free modules,\ $S$-Noetherian modules etc. ...

an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

If R is a commutative ring, then we prove that every finitely generated R-module has a pure-composition series with indecomposable cyclic factors and any two such series are isomorphic if and only if R is a Bézout ring and a CF-ring. When R is a such ring, the length of a pure-composition series of a finitely generated R-module M is compared with its Goldie dimension and we prove that these num...

The main goal of this paper is to study the lattice of T L-submodules of a module. It is well-known that the lattice of submodules of a module is modular. In this study, we prove an analogous result for L-sets that is the lattice of L-submodules of a module is modular for an infinitely ∨-distributive lattice.