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On a Product of Finite Monoids

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: In this paper, for each positive integer m, we associate with a finite monoid S0 and m finite commutative monoids S1,…, Sm, a product ◊m(Sm,…, S1, S0). We give a representation of the free objects in the pseudovariety ◊m(Wm,…, W1, W0) generated by these (m + 1)-ary products where SiWi for all 0 ≤ i ≤ m. We then give, in particular, a criterion to determine when an identity holds in ◊m(J1,…, J1, J1) with the help of a version of the Ehrenfeucht-Fraïssé game (J1 denotes the pseudovariety of all semilattice monoids). The union ∪m>0m (J1,…, J1, J1) turns out to be the second level of the Straubing’s dot-depth hierarchy of aperiodic monoids.

Additional Information

Publication
Semigroup Forum, Vol. 57, 1998, pp 75-91.
Language: English
Date: 1998
Keywords
Integers, Monoids, Identity, Mathematics