Equations on Semidirect Products of Commutative Semigroups
نویسندگان
چکیده
In this paper; we study equations on semidirect products of commutative semigroups. Let Comq,r denote the pseudovariety of all finite semigroups that satisfy the equations xy = yx and x r + q = xr. The pseudovariety Com1,1 is the pseudovariety of all finite semilattices. We consider the product pseudovariety Comq,r * generated by all semidirect products of the form S*T with S ∈ Comq,r and T ∈ ,. We give an algorithm to decide when an equation holds in Comq,r * . Finite complete sets of equations are described for all the products Comq,r * which provide polynomial time algorithms to test membership. Our results imply finite complete sets of equations for Gcom * Com1,1 and (Com⋂A) *Com1,1 (among others). Here; Gcom denotes the pseudovariety of all finite commutative groups; Com the pseudovariety of all finite commutative semigroups and A the pseudovariety of all finite aperiodic semigroups. Article:
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