Journal of Combinatorial Algebra

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Volume 1, Issue 4, 2017, pp. 341–370
DOI: 10.4171/JCA/1-4-1

Published online: 2017-10-09

Multifraction reduction III: The case of interval monoids

Patrick Dehornoy[1] and Friedrich Wehrung[2]

(1) Université de Caen, France
(2) Université de Caen, France

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 problemfor 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 reductionwithout convergence, semi-convergence up to some level but not beyond, non-embeddability into the enveloping group (a strong negation of semi-convergence).

Keywords: Poset, intervalmonoid, gcd-monoid, enveloping group, word problem,multifraction, reduction, embeddability, semi-convergence, circuit, zigzag

Dehornoy Patrick, Wehrung Friedrich: Multifraction reduction III: The case of interval monoids. J. Comb. Algebra 1 (2017), 341-370. doi: 10.4171/JCA/1-4-1