Automorphisms of the semigroup of all endomorphisms of free algebras

Details Automorphisms of the semigroup of all endomorphisms of free algebras Automorphisms of the semigroup of all endomorphisms of free algebras

2005-10-11

arxiv.org/abs/math/0510230v1

Mathematics

General Mathematics

17 pages

Scientific paper

Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups, modules, Lie algebras and some others. All these researches were inspired by the questions prof. B. Plotkin set in connection with so called universal algebraic geometry (see for example Arxiv:math, GM/0204245). The aim of this paper is to suggest a method of describing the group AutEnd(F) for a free finitely generated algebra F of an arbitrary variety of universal algebras. This method allows to obtain easily all known results as well as new ones.

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