Unary enhancements of inherently non-finitely based semigroups
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This paper is a follow up of an article published in 2012 by three of the authors, more precisely, of a part of that article dealing with inherently nonfinitely based involutory semigroups. We exhibit a simple condition under which a finite involutory semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semigroup. As applications, we get already known as well as new examples of inherently nonfinitely based involutory semigroups. We also show that for finite regular semigroups, our condition is not only sufficient but also necessary for the property of being inherently nonfinitely based to persist. This leads to an algorithmic description of regular inherently nonfinitely based involutory semigroups.
KeywordsInvolutory semigroup Inherently nonfinitely based semigroup Twisted semilattice Twisted Brandt monoid Regular semigroup Matrix semigroup
The authors are indebted to an anonymous referee for several inspiring remarks that have led to an improved presentation of Sect. 4.
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