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

Dipak Ravindra Bonde

Department of Mathematics, ACS College, Dharangaon-425105, India

E-mail Address: drbonde@rediffmail.com

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and

Jayprakash Ninu Chaudhari

Department of Mathematics, M. J. College, Jalgaon-425002, India

E-mail Address: jnchaudhari@rediffmail.com

Corresponding author.

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https://doi.org/10.1142/S179355712150128XCited by:0 (Source: Crossref)

Abstract

Characterizations of $α$ $α$ -prime ideals, weakly $α$ $α$ -prime ideals in a semiring $R$ $R$ are investigated. If $I$ $I$ is a $Q$ $Q$ -ideal of a semiring $R$ $R$ , then a relation between the set of $α$ $α$ -prime ideals (weakly $α$ $α$ -prime ideals) in $R$ $R$ and the set of $α$ $α$ -prime ideals (weakly $α$ $α$ -prime ideals) in the quotient semiring $R / I_{(Q)}$ $R / I_{(Q)}$ is obtained.

Communicated by N. Gilbert

Keywords:

AMSC: 16Y60

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