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arXiv · 1607.00099

k-Congruences on semirings

Song-Chol Han
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Abstract

For any semiring, the concept of k-congruences is introduced, criteria for k-congruences are established, it is proved that there is an inclusion-preserving bijection between k-congruences and k-ideals, and an equivalent condition for the existence of a zero is presented with the help of k-congruences. It is shown that a semiring is k-simple iff it is k-congruence-simple, and that inclines are k-simple iff they have at most 2 elements. Lemma 2.12(i) in [Glas. Mat. 42(62) (2007) 301] is pointed out being false.

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Song-Chol Han. 2016-07-01. k-Congruences on semirings. https://arxiv.org/abs/1607.00099

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