Multifraction reduction III: The case of interval monoids
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 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).
Keywords
Cite
@article{arxiv.1606.09018,
title = {Multifraction reduction III: The case of interval monoids},
author = {Patrick Dehornoy and Friedrich Wehrung},
journal= {arXiv preprint arXiv:1606.09018},
year = {2017}
}
Comments
23 pages ; v2 : cross-references updated ; v3 : one example added, typos corrected; final version due to appear in Journal of Combinatorial Algebra