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,…, S_m, a product ◊_m(S_m,…, S₁, S₀). We give a representation of the free objects in the pseudovariety ◊_m(W_m,…, W₁, W₀) generated by these (m + 1)-ary products where S_i ∈ W_i 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>0◊_m (J₁,…, J₁, J₁) turns out to be the second level of the Straubing’s dot-depth hierarchy of aperiodic monoids.

On a Product of Finite Monoids
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Additional Information

Publication

Semigroup Forum, Vol. 57, 1998, pp 75-91.

Language: English

Date: 1998

Keywords

Integers, Monoids, Identity, Mathematics

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