Submodules Satisfying the Uniformly Classical S-Primary Property

Naji O. A., YILDIZ YILMAZ E., Özen M., TEKİR Ü.

Journal of Mathematics, vol.2026, no.1, 2026 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2026 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1155/jom/6349278
  • Journal Name: Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: classical S-primary submodules, uniformly classical S-primary submodule, uniformly primary submodules
  • Yıldız Technical University Affiliated: Yes

Abstract

We define uniformly classical S-primary submodules, where S is a multiplicatively closed subset. A submodule W of an H-module E with (W:HE)∩S = ∅ is said to be a uniformly classical S-primary submodule if ∃s ∈ S and (Formula presented.) such that whenever ηγν ∈ W for η, γ ∈ H, ν ∈ E, then sην ∈ W or (sγ)kν ∈ W. We investigate many properties of this new type of submodules and give relations with the other submodules. We provide various characterizations of this class of submodules in terms of other submodules and ideals. Moreover, we study the notion under homomorphisms, in factor modules, Cartesian product, localization, idealization, and amalgamation modules along an ideal with respect to a homomorphism.