Generalizations of 2-absorbing and 2-absorbing primary submodules

MOSTAFANASAB H., TEKİR Ü., Celikel E. Y., Ugurlu E., ULUCAK G., DARANI A. Y.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.4, pp.1001-1016, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.15672/hjms.2018.577
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1001-1016
  • Keywords: phi-prime submodule, phi-primary submodule, 2-absorbing primary submodule, weakly 2-absorbing primary submodule, phi-2-absorbing submodule, phi-2-absorbing primary submodule, PRIMARY IDEALS, IDEMPOTENT
  • Marmara University Affiliated: Yes

Abstract

In this study, we introduce phi-2-absorbing and phi-2-absorbing primary submodules of modules over commutative rings generalizing the concepts of 2-absorbing and 2-absorbing primary submodules. Let phi : S(M) -> S(M) boolean OR {phi} be a function where S(M) denotes the set of all submodules of M and N a proper submodule of an R-module M. We will say that N is a phi-2-absorbing submodule of M if whenever a, b is an element of R, m is an element of M with abm is an element of N and abm (sic) phi(N), then am is an element of N or bm is an element of N or ab is an element of (N :(R) M) and N is said to be a phi-2-absorbing primary submodule of M whenever if a, b is an element of R, m is an element of M with abm is an element of N and abm (sic) phi(N), then am is an element of M-rad(N) or bm is an element of M-rad(N) or ab is an element of (N :(R) M). We investigate many properties of these new types of submodules and establish some characterizations for phi-2-absorbing and phi-2-absorbing primary submodules of multiplication modules.