# Equations on the semidirect product of a finite semilattice by a finite commutative monoid

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

Abstract: Let Comt,q denote the variety of finite monoids that satisfy the equations xy = yx and xt = xt+q . The variety Com1,1 is the variety of finite semilattices also denoted by J1. In this paper, we consider the product variety J1*Comt,q generated by all semidirect products of the form M * N with MJ1 and NComt,q. We give a complete sequence of equations for J1 * Comt,q implying complete sequences of equations for J1 * (ComA), J1 * (ComG) and J1 * Com, where Com denotes the variety of finite commutative monoids, A the variety of finite aperiodic monoids and G the variety of finite groups.
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