The Join of the Pseudovariety J with Permutative Pseudovarieties
Using a theorem of Reiterman, which characterizes pseudovarieties as classes of finite semigroups satisfying a set of pseudoidentities, and a characterization of the implict operations on DS, we calculate some joins of the form J∨ V, where V is a permutative pseudovariety. As a consequence we obtain that, for these V, J ∨ V is decidable if and only if V ∩ CS is decidable.
KeywordsSemi Group Topological Semigroup Hasse Diagram Finite Semigroup Implicit Operation
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