Dehornoy, Patrick A cancellativity criterion for presented monoids. (English) Zbl 07127651 Semigroup Forum 99, No. 2, 368-390 (2019). Summary: We establish a new, fairly general cancellativity criterion for a presented monoid that properly extends the previously known related criteria. It is based on a new version of the word transformation called factor reversing, and its specificity is to avoid any restriction on the number of relations in the presentation. As an application, we deduce the cancellativity of some natural extension of Artin’s braid monoid in which crossings are colored. Cited in 1 Document MSC: 20M Semigroups Keywords:semigroup presentation; Van Kampen diagram; rewrite system; cancellativity; word problem; garside monoid; group of fractions; monoid embeddability; Artin-Tits groups PDF BibTeX XML Cite \textit{P. Dehornoy}, Semigroup Forum 99, No. 2, 368--390 (2019; Zbl 07127651) Full Text: DOI References: [1] Adyan, S.I.: On the embeddability of monoids. Soviet. Math. Dokl. 1-4, 819-820 (1960) · Zbl 0114.25305 [2] Berenstein, A., Greenberg, J., Li, J.R.: Monomial braidings; in preparation. http://www.wisdom.weizmann.ac.il/ jianrong/mon_braid_fin.pdf. Accessed 01 Nov 2017 [3] Birman, J.: Braids, links, and mapping class groups. Princeton University Press, Princeton, NJ (1974) [4] Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups, vol. 1. American Mathematical Society, Providence, RI (1961) · Zbl 0111.03403 [5] Dehornoy, P.: Groups with a complemented presentation. J. Pure Appl. Algebra 116, 115-137 (1997) · Zbl 0870.20023 [6] Dehornoy, P.: On completeness of word reversing. Discrete Math. 225, 93-119 (2000) · Zbl 0966.05038 [7] Dehornoy, P.: Complete positive group presentations. J. Algebra 268, 156-197 (2003) · Zbl 1067.20035 [8] Dehornoy, P.: The subword reversing method. Int. J. Algebra Comput. 21, 71-118 (2011) · Zbl 1256.20053 [9] Dehornoy, P.: Multifraction reduction I: The 3-ore case and Artin-Tits groups of type FC. J. Comb. Algebra 1, 185-228 (2017) · Zbl 1422.20020 [10] Dehornoy, P., Wiest, B.: On word reversing in braid groups. Int. J. Algebra Comput. 16(5), 931-947 (2006) · Zbl 1114.20021 [11] Garside, F.A.: The braid group and other groups. Q. J. Math. Oxf. 20-78, 235-254 (1969) · Zbl 0194.03303 [12] Higgins, P.: Techniques of Semigroup Theory. Oxford University Press, Oxford (1992) · Zbl 0744.20046 [13] Ore, Ø.: Linear equations in non-commutative fields. Ann. Math. 32, 463-477 (1931) · Zbl 0001.26601 [14] Remmers, J.H.: On the geometry of semigroup presentations. Adv. Math. 36, 283-296 (1980) · Zbl 0438.20041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.