S-k-primary ideals of semirings

Resumo

Let R be a commutative ring and S ⊊ R be a multiplicatively closed set. Essebti Massaoud[9] defined a proper ideal Q of R disjoint from S to be S-primary ideal of
R if there exists an s ∈ S such that for all a, b ∈ R if ab ∈ Q then sa ∈ Q or sb ∈ Rad(Q). In this paper, we introduce the notion of S-k-primary ideal of a semiring.
We present some analogous results of primary and k-primary ideals of a semiring that S-k-primary ideal enjoy. We also study the properties of Rad(Q) if Q is an
S-k-primary ideal of a semiring. We further study the form of S-k-primary ideals in the amalgamation of semirings R₁ with R₂ along an ideal J of R₂ with respect to
a morphism f, introduced and studied by D’Anna et al.[3] and extended by Essebti Massaoud for S-primary ideal of a ring.