Theoretical Foundations of Applied Discrete Mathematics

On the regularity of some subsemigroups of equivalence relation's endomorphism monoid

E. A. Bondar

Luhansk Taras Schevchenko State Pedagogical University, Lugansk, Ukraine

Abstract: For the set of halfstrong (locally strong, quasi-strong) endomorphisms of an equivalence relation graph, the conditions to form a semigroup are found. Thus the answer to the question put by M. Böttcher and U. Knauer's is given. The conditions for regularity of such semigroups are found too.

Keywords: regularity, semigroup, endomorphism, equivalence.

UDC: 512.53