Abstract
The object of this study is the second-type annihilation predicate α: (a, b) ∈ a ⇔ ab = ba = a, b2 = b. In terms of identities, we give a complete description of varieties of semigroups which are finitely approximable with respect to this predicate. Another subject considered in this work is the problem of algorithmic decidability of the predicate. Solution of this problem is related to finite semigroups the absence of which in the variety is the condition for existence of the corresponding algorithm. Our proof relies on results of M. Petrich, A.I. Mal’tsev, E.A. Golubov, M.V. Sapir, and S.I. Kublanovskii.
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