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Article Dans Une Revue Journal of Combinatorial Algebra Année : 2017

Multifraction reduction III: The case of interval monoids

Résumé

We investigate gcd-monoids, which are cancellative monoids in which any two elements admit a left and a right gcd, and the associated reduction of multifractions (arXiv:1606.08991 and 1606.08995), a general approach to the word problem for the enveloping group. Here we consider the particular case of interval monoids associated with finite posets. In this way, we construct gcd-monoids, in which reduction of multifractions has prescribed properties not yet known to be compatible: semi-convergence of reduction without convergence, semi-convergence up to some level but not beyond, non-embeddability into the enveloping group (a strong negation of semi-convergence).
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Dates et versions

hal-01338434 , version 1 (28-06-2016)
hal-01338434 , version 2 (01-07-2016)
hal-01338434 , version 3 (30-01-2017)

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Patrick Dehornoy, Friedrich Wehrung. Multifraction reduction III: The case of interval monoids. Journal of Combinatorial Algebra, 2017, 1 (4), pp.341--370. ⟨hal-01338434v3⟩
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