Elsevier

Journal of Algebra

Volume 369, 1 November 2012, Pages 203-225
Journal of Algebra

Equational theories of semigroups with involution

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Abstract

We employ the techniques developed in an earlier paper to show that involutory semigroups arising in various contexts do not have a finite basis for their identities. Among these are partition semigroups endowed with their natural inverse involution, including the full partition semigroup Cn for n2, the Brauer semigroup Bn for n4 and the annular semigroup An for n4, n even or a prime power. Also, all of these semigroups, as well as the Jones semigroup Jn for n4, turn out to be inherently nonfinitely based when equipped with another involution, the ‘skew’ one. Finally, we show that similar techniques apply to the finite basis problem for existence varieties of locally inverse semigroups.

MSC

20M07
03C05

Keywords

(Non)finitely based algebraic structure
Involutory semigroup
Partition semigroup
Existence variety

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