On S-2-absorbing submodules and vn-regular modules

Ulucak G., TEKİR Ü., KOÇ S.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, vol.28, no.2, pp.239-257, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.2478/auom-2020-0030
  • Journal Name: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.239-257
  • Keywords: 2-absorbing submodule, S-2-absorbing submodule, von Neumann regular module, 2-ABSORBING PRIMARY SUBMODULES, MORPHIC RINGS
  • Marmara University Affiliated: Yes

Abstract

Let R be a commutative ring and M an R-module. In this article, we introduce the concept of S-2-absorbing submodule. Suppose that S subset of R is a multiplicatively closed subset of R. A submodule P of M with (P :(R) M) boolean AND S = empty set is said to be an S-2-absorbing submodule if there exists an element s is an element of S and whenever abm is an element of P for some a, b is an element of R and m is an element of M, then sab is an element of (P :(R) M) or sam is an element of P or sbm is an element of P. Many examples, characterizations and properties of S-2-absorbing submodules are given. Moreover, we use them to characterize von Neumann regular modules in the sense [9].