Weakly Classical Prime Submodules

Mostafanasab H., TEKİR Ü., Oral K. H.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.56, no.4, pp.1085-1101, 2016 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.5666/kmj.2016.56.4.1085
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.1085-1101
  • Keywords: Weakly prime submodule, Classical prime submodule, Weakly classical prime submodule, 2-ABSORBING PRIMARY IDEALS
  • Marmara University Affiliated: Yes

Abstract

In this paper, 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 "weakly classical prime submodules" and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule N of M is a weakly classical prime submodule if whenever a, b is an element of R and m is an element of M with 0 not equal abm is an element of N, then am is an element of N or bm is an element of N.