2020•Asian-European Journal of MathematicsRequires access

On α-prime and weakly α-prime ideals in semirings

Dipak Ravindra Bonde, Jayprakash Ninu Chaudhari

Abstract

Characterizations of [Formula: see text]-prime ideals, weakly [Formula: see text]-prime ideals in a semiring [Formula: see text] are investigated. If [Formula: see text] is a [Formula: see text]-ideal of a semiring [Formula: see text], then a relation between the set of [Formula: see text]-prime ideals (weakly [Formula: see text]-prime ideals) in [Formula: see text] and the set of [Formula: see text]-prime ideals (weakly [Formula: see text]-prime ideals) in the quotient semiring [Formula: see text] is obtained.

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Key concepts: Prime (order theory), Mathematics, Ideal (ethics), Quotient, Semiring, Associated prime, Prime element, Semiprime ring