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Ideals and congruences in pseudo-BCH algebras. (English) Zbl 1496.06022

Summary: We introduce the concept of a translation ideal in pseudo-BCH algebras and investigate its properties. We prove that for any pseudo-BCH algebra \(\mathfrak X\) there is a one-to-one order-preserving correspondence between the closed translation ideals of \(\mathfrak X\) and the relative congruences on \(\mathfrak X\).

MSC:

06F35 BCK-algebras, BCI-algebras
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