JournalsjcaVol. 1 , No. 4pp. 341–370

Multifraction reduction III: The case of interval monoids

  • Patrick Dehornoy

    Université de Caen, France
  • Friedrich Wehrung

    Université de Caen, France
Multifraction reduction III: The case of interval monoids cover
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Abstract

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).

Cite this article

Patrick Dehornoy, Friedrich Wehrung, Multifraction reduction III: The case of interval monoids. J. Comb. Algebra 1 (2017), no. 4 pp. 341–370

DOI 10.4171/JCA/1-4-1