Classical 2-Absorbing Submodules of Modules over Commutative Rings

Mostafanasab H., TEKİR Ü., Oral K. H.

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, vol.8, no.3, pp.417-430, 2015 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 3
  • Publication Date: 2015
  • Journal Name: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.417-430
  • Keywords: Classical prime submodule, Classical 2-absorbing submodule, PRIME SUBMODULES, PRIMARY IDEALS
  • Marmara University Affiliated: Yes

Abstract

In this article, all rings are commutative with nonzero identity. Let M be an R- module. A proper submodule N of M is called a classical prime submodule, if for each m is an element of M and elements a, b is an element of R, abm is an element of N implies that am is an element of N or bm is an element of N. We introduce the concept of " classical 2- absorbing submodules" as a generalization of "classical prime submodules". We say that a proper submodule N of M is a classical 2-absorbing submodule if whenever a, b, c is an element of R and m is an element of M with abcm is an element of N, then abm is an element of N or acm is an element of N or bcm is an element of N.