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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Automorphisms of the endomorphism semigroup of a free monoid or a free semigroup


Authors: G. Mashevitzky and Boris M. Schein
Journal: Proc. Amer. Math. Soc. 131 (2003), 1655-1660
MSC (1991): Primary 20M20, 20M05, 08A35
Published electronically: January 15, 2003
MathSciNet review: 1953569
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Abstract: We determine all isomorphisms between the endomorphism semigroups of free monoids or free semigroups and prove that automorphisms of the endomorphism semigroup of a free monoid or a free semigroup are inner or ``mirror inner". In particular, we answer a question of B. I. Plotkin.


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Additional Information

G. Mashevitzky
Affiliation: Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva, Israel
Email: gmash@math.bgu.ac.il

Boris M. Schein
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email: bschein@uark.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06923-5
PII: S 0002-9939(03)06923-5
Keywords: Free semigroup, free monoid, endomorphism, automorphism
Received by editor(s): December 5, 2001
Published electronically: January 15, 2003
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2003 American Mathematical Society