Equations on Semidirect Products of Commutative Semigroups

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Francine Blanchet-Sadri, Professor (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: 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 xr + q = xr. The pseudovariety Com1,1 is the pseudovariety of all finite semilattices. We consider the product pseudovariety Comq,r * Comq',r' generated by all semidirect products of the form S * T with S ∈ Comq,r and T ∈ Comq',r'. We give an algorithm to decide when an equation holds in Comq,r * Comq',r'. Finite complete sets of equations are described for all the products Comq,r * 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.

Additional Information

Semigroup Forum 55(1), 80-88.
Language: English
Date: 1997
Mathematics, Computer science, Products, Commutative

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