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Proceedings of the American Mathematical Society

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On maximal $ k$-ideals of semirings


Authors: M. K. Sen and M. R. Adhikari
Journal: Proc. Amer. Math. Soc. 118 (1993), 699-703
MSC: Primary 16Y60
DOI: https://doi.org/10.1090/S0002-9939-1993-1132423-6
MathSciNet review: 1132423
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Abstract: For a semiring $ S$ with commutative addition, conditions are considered such that $ S$ has nontrivial $ k$-ideals or maximal $ k$-ideals, among others, by the help of the congruence class semiring $ S/A$ defined by an ideal $ A$ of $ S$. Moreover, all maximal $ k$-ideals of the semiring of nonnegative integers are described.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1132423-6
Keywords: Semiring, $ k$-ideals, maximal $ k$-ideals, completely prime $ k$-ideals
Article copyright: © Copyright 1993 American Mathematical Society