Glasnik Matematicki, Vol. 43, No.1 (2008), 13-23.

ON PRIMAL AND WEAKLY PRIMAL IDEALS OVER COMMUTATIVE SEMIRINGS

Shahabaddin Ebrahimi Atani

Abstract.   Since the theory of ideals plays an important role in the theory of semirings, in this paper we will make an intensive study of the notions of primal and weakly primal ideals in commutative semirings with an identity 1. It is shown that these notions inherit most of the essential properties of the primal and weakly primal ideals of a commutative ring with non-zero identity. Also, the relationship among the families of weakly prime ideals, primal ideals and weakly primal ideals of a semiring R is considered.

2000 Mathematics Subject Classification.   16Y60.

Key words and phrases.   Semiring, weakly prime, primal, weakly primal.

DOI: 10.3336/gm.43.1.03

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