Automorphisms of endomorphism monoids of 1-Simple free algebras

Konieczny, Janusz; Araújo, João

http://hdl.handle.net/10400.2/2004

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Authors

Konieczny, Janusz

Araújo, João

Abstract(s)

For any set X and any variety V of algebras, let A = A_V(X) be the free algebra in V with set X of free generators, and let End(A) be the monoid of endomorphisms of A. We provide a general approach to the description of the automorphism group of End(A), and some subsemigroups of End(A), provided that A is 1-simple. We show that every automorphism of End(A) is a unique extension of an automorphism of the monoid of endomorphisms of rank at most 1.

Keywords

Automorphisms Endomorphisms Free Independent Monoids Simple Universal algebras

URI

http://hdl.handle.net/10400.2/2004

Citation

Konieczny, Janusz; Araújo, João - Automorphisms of endomorphism monoids of 1-Simple free algebras. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 37, nº 1 (2011), p. 83-94