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, cilt.46, sa.2, ss.421-427, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s40995-022-01271-z
  • Dergi Adı: Iranian Journal of Science and Technology, Transaction A: Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, Communication Abstracts, zbMATH
  • Sayfa Sayıları: ss.421-427
  • Anahtar Kelimeler: Primary submodule, Prime submodule, ϕ-Prime, ϕ-δ-Primary submodule
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

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.