Identity Problems, Solvability of Equations and Unification in Varieties of Semigroups Related to Varieties of Groups

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Authors

KLÍMA Ondřej POLÁK Libor

Year of publication 2011
Type Article in Proceedings
Conference Algebraic Foundations in Computer Science
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1007/978-3-642-24897-9_10
Field General mathematics
Keywords identity problems; equations; unification; varieties of semigroups; varieties of unary semigroups
Description In this survey we consider three kinds of algorithmic questions concerning varieties of semigroups. We are interested in identity problems, in the solvability of a system of equations and in the structure of all solutions of a given system. We study them in significant varieties of semigroups, monoids, groups, completely simple semigroups, completely regular semigroups (in particular semigroups satisfying the identity x^r=x) and involutary semigroups (in particular star regular semigroups and inverse semigroups).
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