r-Submodules and sr-Submodules

Koç S., Tekir Ü.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.4, pp.1863-1876, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1702-20
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1863-1876
  • Keywords: r-Ideal, prime ideal, r-submodule, special r-submodule, prime submodule, PRIME SUBMODULES


In this article, we introduce new classes of submodules called r-submodule and special r-submodule, which are two different generalizations of r-ideals. Let M be an R-module, where R is a commutative ring. We call a proper submodule N of M an r-submodule (resp., special r-submodule) if the condition am is an element of N with ann(M) (a) = 0(M) (resp., ann(R)(m) = 0) implies that m E N (resp., a is an element of (N :(R) M)) for each a is an element of R and m is an element of M. We also give various results and examples concerning r-submodules and special r-submodules.