Geodesic
Quasi-primary ideals in commutative semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 101-110

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In this paper, we define quasi-primary ideals in commutative semirings S with 1 0 which is a generalization of primary ideals. A proper ideal I of a semiring S is said to be a quasi-primary ideal of S if ab∈√(I) implies a∈√(I) or b∈√(I). We also introduce the concept of 2-absoring quasi-primary ideal of a semiring S which is a generalization of quasi-primary ideal of S. A proper ideal I of a semiring S is said to be a 2-absorbing quasi-primary ideal if abc∈√(I) implies ab∈√(I) or bc∈√(I) or ac∈√(I). Some basic results related to 2-absorbing quasi-primary ideal have also been given.
Keywords: semiring, subtractive ideal, primary ideal, quasi-primary ideal, $2$-absorbing quasi-primary ideal, $Q$-ideal 
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Sarohe, Poonam; Kumar, Pratibha. Quasi-primary ideals in commutative semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 101-110. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_1_a8/