×

Semigroups of endomorphisms of some infinite monounary algebras. (Russian, English) Zbl 1274.08023

Mat. Metody Fiz.-Mekh. Polya 55, No. 1, 29-38 (2012); translation in J. Math. Sci., New York 190, No. 5, 658-668 (2013).
A class of infinite monounary algebras (see [A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Volume 1. Providence, R.I.: American Mathematical Society (AMS) (1961; Zbl 0111.03403)]) without cyclic and metamonogenic subalgebras is considered. It is shown that monounary algebra of this class is determined up to isomorphism by its semigroup of endomorphisms. It is also proved that in the semigroup of endomorphisms of each monounary algebra of the class there is a tightly embedded ideal, the cardinal number of which equals to the order of this monounary algebra and also defines it.

MSC:

08A60 Unary algebras
08A35 Automorphisms and endomorphisms of algebraic structures
20M30 Representation of semigroups; actions of semigroups on sets
PDFBibTeX XMLCite