Напівгрупа слабких ендоморфізмів відношення часткової еквівалентності

Yu. Zhuchok; О. Toichkina

doi:10.3842/umzh.v76i12.8412

Yu. Zhuchok Luhansk Taras Shevchenko National University, Poltava; Johannes Kepler University in Linz, Austria
О. Toichkina Luhansk Taras Shevchenko National University, Poltava

DOI: https://doi.org/10.3842/umzh.v76i12.8412

Abstract

UDC 512.53

We study the weak endomorphism semigroup of a partial equivalence relation. We describe necessary and sufficient conditions for the existence of these endomorphisms and, in general, endotopisms. We establish the conditions under which the set of all idempotents of the weak endomorphism semigroup of a strict partial equivalence is its subsemigroup, as well as the conditions of regularity and coregularity of the weak endomorphism semigroup. In terms of the wreath product of a symmetric transformation semigroup and a small category, we describe a faithful representation of the weak endomorphism semigroup of an arbitrary relation of a strict partial equivalence.

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Semigroup of weak endomorphisms of a partial equivalence relationship

Abstract

References