Discussiones Mathematicae General Algebra and Applications, Dec 31, 2024
Let R be a commutative ring and S a multiplicatively closed subset of R. Hamed and Malek [7] defi... more Let R be a commutative ring and S a multiplicatively closed subset of R. Hamed and Malek [7] defined an ideal P of R disjoint with S to be an S-prime ideal of R if there exists an s ∈ S such that for all a, b ∈ R if ab ∈ P, then sa ∈ P or sb ∈ P. In this paper, we introduce the notions of S-k-prime and S-k-semiprime ideals of semirings, S-k-m-system, and S-k-p-system. We study some properties and characterizations for S-k-prime and S-k-semiprime ideals of semirings in terms of S-k-m-system and S-kp-system respectively. We also introduce the concepts of S-prime semiring and S-semiprime semiring and study the characterizations for S-k-prime and S-k-semiprime ideals in these two semirings.
Discussiones Mathematicae General Algebra and Applications, Dec 31, 2024
Let R be a commutative ring and S a multiplicatively closed subset of R. Hamed and Malek [7] defi... more Let R be a commutative ring and S a multiplicatively closed subset of R. Hamed and Malek [7] defined an ideal P of R disjoint with S to be an S-prime ideal of R if there exists an s ∈ S such that for all a, b ∈ R if ab ∈ P, then sa ∈ P or sb ∈ P. In this paper, we introduce the notions of S-k-prime and S-k-semiprime ideals of semirings, S-k-m-system, and S-k-p-system. We study some properties and characterizations for S-k-prime and S-k-semiprime ideals of semirings in terms of S-k-m-system and S-kp-system respectively. We also introduce the concepts of S-prime semiring and S-semiprime semiring and study the characterizations for S-k-prime and S-k-semiprime ideals in these two semirings.
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