Semigroups of Strong Endomorphisms of Infinite Graphs and Hypergraphs
We define a class of infinite undirected graphs and a class of infinite $n$-regular hypergraphs and prove that any semigroup of all strong endomorphisms of the graphs and hypergraphs from these classes is isomorphic to the wreath product of a transformation monoid and a small category. We establish the criterional conditions for the regularity of the semigroup of strong endomorphisms of infinite $n$-regular hypergraphs.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 6, pp 823-834.
Citation Example: Bondar’ E. A. Semigroups of Strong Endomorphisms of Infinite Graphs and Hypergraphs // Ukr. Mat. Zh. - 2013. - 65, № 6. - pp. 743–754.