t-PRIME SUBMODULES


Moghaderi J., TERCAN A.

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, vol.84, no.3, pp.31-40, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 84 Issue: 3
  • Publication Date: 2022
  • Journal Name: UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.31-40
  • Keywords: prime submodule, primary submodule, n-submodule, IDEALS
  • Hacettepe University Affiliated: Yes

Abstract

Let R be a commutative ring with identity. For t is an element of N, a proper submodule N of an R-module M is called a t-prime submodule if rm is an element of N (r is an element of R, m is an element of M), then m is an element of N or r(t) is an element of(N :(R) M). We show that any maximal t-prime submodule, with respect to inclusion, is prime and a proper submodule is a t-prime submodule if and only if its quotient module is t-torsion free. We obtain some characterizations of t-prime submodules. Also various properties of t-prime submodules are investigated. We provide several examples which illustrate our results.