This article is cited in 3 papers

RESEARCH ARTICLE

The monoid of endomorphisms of disconnected hypergraphs

Yuriy V. Zhuchok

Department of Mathematical Analysis and Algebra, Luhansk Taras Shevchenko National University, Oboronna str., 2, 91011 Luhansk, Ukraine

Abstract: We prove that the monoid of endomorphisms of an arbitrary disconnected hypergraph is isomorphic to a wreath product of a transformation semigroup with a certain small category. For disconnected hypergraphs we also study the structure of the monoid of strong endomorphisms and the group of automorphisms.

Keywords: monoid of endomorphisms, monoid of strong endomorphisms, group of automorphisms, hypergraph, wreath product.

MSC: 08A05

Received: 13.02.2012
Revised: 30.03.2013

Language: English

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