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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The $k$-closure of monic and monic free ideals in a polynomial semiring

Author: Louis Dale
Journal: Proc. Amer. Math. Soc. 64 (1977), 219-226
MSC: Primary 16A78
MathSciNet review: 0444717
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Abstract: The concepts of k-closure, k-boundary and weak k-ideals are introduced and necessary and sufficient conditions that an ideal be a k-ideal are given. These conditions are applied to monic and monic free k-ideals. Also, it is shown that the ascending chain condition holds for monic ideals, but not for monic free ideals, and that a semiring S is Noetherian if and only if $S[x]$ satisfies the ascending chain condition for monic ideals.

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Keywords: Strict semiring, monic ideals, monic free ideals, <I>k</I>-ideals, weak <I>k</I>-ideals, <I>k</I>-closure, <I>k</I>-boundary
Article copyright: © Copyright 1977 American Mathematical Society