Geodesic
$S$−$k$−prime and $S$−$k$−semiprime ideals of semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 301-317

Voir la notice de l'article provenant de la source Library of Science

Let R be a commutative ring and S a multiplicatively closed subset of R. Hamed and Malek 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-k-p-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.
Keywords: Semiring, $S$−$k$prime ideal, $S$−$k$−semiprime ideal, $S$−prime semiring, $S$−semiprime semiring 
@article{DMGAA_2024_44_2_a4,
     author = {Bhowmick, Sumon and Goswami, Jituparna and Kar, Sukhendu},
     title = {$S$\ensuremath{-}$k$\ensuremath{-}prime and $S$\ensuremath{-}$k$\ensuremath{-}semiprime ideals of semirings},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {301--317},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a4/}
}
TY  - JOUR
AU  - Bhowmick, Sumon
AU  - Goswami, Jituparna
AU  - Kar, Sukhendu
TI  - $S$−$k$−prime and $S$−$k$−semiprime ideals of semirings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2024
SP  - 301
EP  - 317
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a4/
LA  - en
ID  - DMGAA_2024_44_2_a4
ER  - 
%0 Journal Article
%A Bhowmick, Sumon
%A Goswami, Jituparna
%A Kar, Sukhendu
%T $S$−$k$−prime and $S$−$k$−semiprime ideals of semirings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2024
%P 301-317
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a4/
%G en
%F DMGAA_2024_44_2_a4
Bhowmick, Sumon; Goswami, Jituparna; Kar, Sukhendu. $S$−$k$−prime and $S$−$k$−semiprime ideals of semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 301-317. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a4/