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- Title
φ-Primary Subsemimodules.
- Authors
Fatahi, F.; Parsa, M. Lotfi; Safakish, R.
- Abstract
Let R be a commutative semiring with identity and M be a unitary Rsemimodule. Let φ : S(M) → S(M) ∪ {∅} be a function, where S(M) is the set of all subsemimodules of M. We say a proper subsemimodule N of M is φ-primary subsemimodule, if r ∈ R, x ∈ M and rx ∈ N − φ(N) imply that r ∈ √(N :R M) or x ∈ N. The notion of φ-primary subsemimodules is a generalization of the concept of primary, weakly primary and φ-prime subsemimodules. We study properties of φ-primary subsemimodules of a semimodule M and related results to those of ring theory.
- Subjects
RING theory; GENERALIZATION; SEMIRINGS (Mathematics)
- Publication
Southeast Asian Bulletin of Mathematics, 2024, Vol 48, Issue 1, p47
- ISSN
0129-2021
- Publication type
Article