Research ArticleNo Access

On partitioning ideals of $(m, n)$ $(m, n)$ -semirings

J. N. Chaudhari

https://orcid.org/0000-0003-3652-2874

Department of Mathematics, M. J. College, Jalgaon (M.S.), P. O. Box 425002, India

E-mail Address: jnchaudhari@rediffmail.com

Corresponding author.

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Harish Nemade

Department of Mathematics, Dhanaji Nana Mahavidyalaya, Faizpur (M.S.), P. O. Box 425503, India

E-mail Address: hgnemade123@rediffmail.com

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, and

Bijan Davvaz

Department of Mathematics, Yazd University, Yazd, Iran

E-mail Address: davvaz@yazd.ac.ir

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https://doi.org/10.1142/S1793557122501443Cited by:1 (Source: Crossref)

Abstract

In this paper, we prove that if $I$ $I$ is a partitioning ideal of an $(m, n)$ $(m, n)$ -semiring $R$ $R$ with respect to two subsets $Q_{1}$ $Q_{1}$ and $Q_{2}$ $Q_{2}$ of $R$ $R$ , then the quotient $(m, n)$ $(m, n)$ -semirings $R / I_{(Q_{1})}$ $R / I_{(Q_{1})}$ and $R / I_{(Q_{2})}$ $R / I_{(Q_{2})}$ are isomorphic. Also, the concepts of maximal homomorphism, steady homomorphism, one-one homomorphism and $N$ $N$ -homomorphism are generalized for $(m, n)$ $(m, n)$ -semirings and obtained relation between them. Finally, the fundamental theorem of semiring homomorphism is generalized for $(m, n)$ $(m, n)$ -semirings.

Communicated by X. Guo

Keywords:

AMSC: 16Y60

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