Abstract
This paper presents a study of the semidirectly closed pseudovariety generated by the aperiodic Brandt semigroup B2, denoted V*(B2). We construct a basis of pseudoidentities for the semidirect powers of the pseudovariety generated by B2 which leads to the main result, which states that V*(B2) is decidable. Independently, using some suggestions given by J. Almeida in his book "Finite Semigroups and Universal Algebra", we constructed an algorithm to solve the membership problem in V* (B2).
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