On free semilattice-ordered semigroups satisfying x
n
=x |
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Authors: | Petr Gajdoš Martin Kuřil |
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Institution: | 1. Katedra matematiky PrF UJEP, Ceske mladeze 8, 400 96, Usti nad Labem, Czech Republic
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Abstract: | Let B(k,0,n) denote the group with k generators which is free in the group variety defined by the identity x
n
=1. Let B
slo
(k,1,n) denote the semilattice-ordered semigroup with k generators which is free in the semilattice-ordered semigroup variety defined by the identity x
n
=x. We prove a generalization of the Green-Rees theorem: B
slo
(k,1,n) is finite for all k≥1 if and only if B(k,0,n−1) is finite for all k≥1. We find a formula for card(B
slo
(1,1,n)). We construct B
slo
(k,1,n) for some concrete values of k and n. |
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Keywords: | |
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