Prime Submodules and Flat Modules Page 1 Acta Mathematica Sinica, English Series Jan.,
2007, Vol. 23, No. 1, pp. 147–152 Published online: Sep. 15, 2006 DOI: 10.1007/s10114-005-0813-0 …

This thesis is aimed at generalizing notions of rings to modules. In particular, notions of
completely prime ideals, s-prime ideals, 2-primal rings and nilpotency of elements of rings …

We introduce the concept of" uniformly primary submodules" of a module over a
commutative ring R, which generalizes the concept of" uniformly primary ideals" of R, a …

It is known that every semiprime ring is a subdirect sum of prime rings. This is a
consequence of the fact that every semiprime ideal is an intersection of prime ideals. We aim …

Let R be a commutative ring with identity and M a unitary R-module. Some properties of
prime submodules of an R-module M have been discussed. In this paper, we investigate the …

The aim of this paper is to introduce the concept of classical weakly prime submodules
which is the generalization of the notion of weakly classical prime submodules to modules …

Let R be a commutative ring with non-zero identity. We define a proper submodule N of an R-
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …

Modules in which every proper submodule (resp. proper nonzero submodule) is prime
(called fully prime (almost fully prime)) and with some other related notions are fully …

Let R be a commutative ring with non-zero identity. We define a proper submodule Nof an R-
module M to be quasi-primary if PM Nrad R=):(is a prime ideal of R. In this case we also say …

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of
prime submodules (that is, second submodules of M) and investigate the conditions under …