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

WEAKLY PRIME SUBMODULES AND PRIME SUBMODULES Page 1 Glasgow Math. J. 48 (2006)
343–346. C 2006 Glasgow Mathematical Journal Trust. doi:10.1017/S0017089506003119 …

In this article, we introduce the dual notions of strongly prime, weakly prime, semiprime, and
primal submodules, that is, strongly second, weakly second, semisecond, and secondal …

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 …

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 …

A proper submodule P of a module M over a ring R is said to be prime if re EP for r ER and
e• M implies that either e• P or r• P: R M. In this paper we investigate the œoIIowing two …

In the first section of this paper the authors give some classes of modules where the two
concepts π and prime are equivalent. Also, they provide conditions under which a given ring …

The purpose of this paper is to investigate pure submodules of multiplication modules. We
introduce the concept of idempotent submodule generalizing idempotent ideal. We show …

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

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 …