1. ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES

M. Ebrahimpour; F. Mirzaee

Volume 5, Issue 2 , Winter and Spring 2018, , Pages 99-109

Abstract
  Abstract. Let m; n ≥ 2 be two positive integers, R a commutative ring with identity and M a unitary R-module. A proper submodule P of M is an (n 􀀀 1; n)-Φm-prime ((n 􀀀 1; n)-weakly prime) submodule if a1; : : : ; an􀀀1 2 R and x 2 M together with a1 : : : an􀀀1x 2 Pn(P : M)m􀀀1P ...  Read More

2. SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

M. Ebrahimpour

Volume 4, Issue 1 , Summer and Autumn 2016, , Pages 15-27

Abstract
  Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed ...  Read More