ON WEAKLY 2-ABSORBING PRIMARY SUBMODULES OF MODULES OVER COMMUTATIVE RINGS

Darani A. Y., Soheilnia F., TEKİR Ü., ULUCAK G.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.54, no.5, pp.1505-1519, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.4134/jkms.j160544
  • Journal Name: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1505-1519
  • Keywords: 2-absorbing submodule, 2-absorbing primary submodule, weakly 2-absorbing primary submodule, PRIMARY IDEALS
  • Marmara University Affiliated: Yes

Abstract

Assume that M is an R-module where R is a commutative ring. A proper submodule N of M is called a weakly 2-absorbing primary submodule of M if 0 not equal abm is an element of N for any a, b is an element of R and m is an element of M, then ab is an element of (N : M) or am is an element of M-rad(N) or bm is an element of M-rad(N). In this paper, we extended the concept of weakly 2-absorbing primary ideals of commutative rings to weakly 2-absorbing primary submodules of modules. Among many results, we show that if N is a weakly 2-absorbing primary submodule of M and it satisfies certain condition 0 not equal I1I2K subset of N for some ideals I-1,I-2 of R and submodule K of M, then I1I2 subset of (N : M) or I1K subset of M-rad(N) or I2K subset of M-rad(N).