Automorphisms of Endomorphism Monoids of 1-Simple Free Algebras
JoΓ£o AraΓΌjo, Janusz Konieczny Β· Communications in Algebra Β· 2009
For any set X and any variety π± of algebras, let π = π π±(X) be the free algebra in π± with set X of free generators, and let End(π) be the monoid of endomorphisms of π. We provide a general approach to the description of the automorphism group of End(π), and some subsemigroups of End(π), provided that π is 1-simple. We show that every automorphism of End(π) is a unique extension of an automorphism of the monoid of endomorphisms of rank at most 1.