A proper submodule N of a module M over a ring R is said to be prime (or P-prime) if re e N
for re R and ee M implies that either ee N or re P= N: M. In other words, N is a prime …

The results of this paper generalize the notion of prime ideal. Consequently, there is defined
prime module and its dual, coprime module. Similarly as the Jacobson radical is defined, we …

Archivum Mathematicum Page 1 Archivum Mathematicum Siamak Yassemi The dual notion
of prime submodules Archivum Mathematicum, Vol. 37 (2001), No. 4, 273--278 Persistent …

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\not= rm\in N $($ r\in R, m\in M $) implies …

0. Introduction. Let R be a ring. A proper left ideal L of R is prime if, for any elements a and b
in R such that aRb CL, either a€ L or b 6 L. For example, any prime two-sided ideal is a …

In this paper we continue our program of studying prime submodules. While the bulk of this
work is devoted to extending results found in [41, additional results independent of those …

A left R-module M is called weakly prime module if the annihilator of any nonzero
submodule of M is a prime ideal and a proper submodule P of M is called weakly prime …

For any associative ring R9 let R1= R when le R; if l φ R, adjoin an identity s usual by R1= Z
χR, Z= 0,±1,±2,.... A submodule Κα M of a right-module M is prime if for any meM and r 6 Jf …

Let R be a ring and M a right R-module. M is called⌖-supplemented if every submodule of M
has a supplement that is a direct summand of M, and M is called completely⌖-supplemented …

The concept of the M-radical of a submodule B< A was defined in [4] as the intersection of all
prime submodules of A containing B. P< A is a prime submodule provided PfA and for reR …