On ϕ - δ -Primary Submodules

ERSOY B. A., TEKİR Ü., Kaya E., Bolat M., KOÇ S.

Iranian Journal of Science and Technology, Transaction A: Science, vol.46, no.2, pp.421-427, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1007/s40995-022-01271-z
  • Journal Name: Iranian Journal of Science and Technology, Transaction A: Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, Communication Abstracts, zbMATH
  • Page Numbers: pp.421-427
  • Keywords: Primary submodule, Prime submodule, ϕ-Prime, ϕ-δ-Primary submodule
  • Marmara University Affiliated: Yes

Abstract

In this paper, we introduce and study a new class of submodules which unify the concepts of prime and primary submodules. Let M be a unital module over a commutative ring R,ϕ:L(M)→L(M)∪{∅} be a reduction function and δ: L(R) → L(R) be an expansion function, where L(M) is the lattice of all submodules of M and L(R) is the lattice of all ideals of R. A proper submodule N of M is said to be a ϕ-δ-primary submodule of M if whenever am∈ N- ϕ(N) for some a∈ R and m∈ M, then either a∈ δ((N: M)) or m∈ N. Many properties, characterizations and examples of ϕ-δ-primary submodules are given.