k-Congruences on semirings
Rings and Algebras
2016-10-04 v1
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.
Cite
@article{arxiv.1607.00099,
title = {k-Congruences on semirings},
author = {Song-Chol Han},
journal= {arXiv preprint arXiv:1607.00099},
year = {2016}
}