On ϕ-δ-Primary Submodules

Ersoy B. A., Tekir Ü., Kaya E., Bolat M., Koç S.

Iranian Journal Of Science And Technology Transaction A-Science, vol.1, pp.1-7, 2022 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 1
  • 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, Agricultural & Environmental Science Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, Communication Abstracts, zbMATH
  • Page Numbers: pp.1-7
  • Yıldız Technical University Affiliated: Yes


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; / : LðMÞ ! LðMÞ[ ;f g be a reduction function and

d : LðRÞ ! LðRÞ be an expansion function, where LðMÞ is the lattice of all submodules of M and LðRÞ is the lattice of all

ideals of R: A proper submodule N of M is said to be a /-d-primary submodule of M if whenever am 2 N  /ðNÞ for some

a 2 R and m 2 M; then either a 2 dððN : MÞÞ or m 2 N: Many properties, characterizations and examples of /-d-primary

submodules are given.