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Unary enhancements of inherently nonfinitely based semigroups
We exhibit a simple condition under which a finite involutary 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.Comment: 11 pages, 1 figure. Section 4 has been improved and expanded
according to suggestions of an anonymous referee of the journal version. A
few minor improvements have been done in Section