On a Product of Finite Monoids By: F. Blanchet-Sadri and F. Dale Gaddis
نویسنده
چکیده
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 Si ∈ Wi 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 (J1,..., J1, J1) turns out to be the second level of the Straubing’s dot-depth hierarchy of aperiodic monoids. Article:
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Trees, Congruences and Varieties of Finite Semigroups By: F. Blanchet-Sadri
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