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2003•Proceedings of the American Mathematical SocietyOpen access

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

Grigory Mashevitzky, Boris M. Schein

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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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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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Available 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.

Key concepts: Endomorphism, Monoid, Automorphism, Semigroup, Bicyclic semigroup, Mathematics, Free monoid, Pure mathematics

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