TY - JOUR
T1 - A countable family of finitely presented infinite congruence-free monoids
AU - Al-Kharousi, Fatma
AU - Cain, Alan J.
AU - Maltcev, Victor
AU - Umar, Abdullahi
N1 - Publisher Copyright:
© 2015 Bolyai Institute, University of Szeged.
PY - 2015
Y1 - 2015
N2 - We prove that the monoids Monha, b, c, d: anb = 0, ac = 1, db = 1, dc = 1, dab = 1, da 2 b = 1,.., dan-1 b = 1i are congruence-free for all n = 1. This provides a new countable family of finitely presented congruence-free monoids, bringing us one step closer to understanding the monoid version of the Boone-Higman Conjecture. We also provide examples showing that finitely presented congruence-free monoids may have quadratic Dehn function.
AB - We prove that the monoids Monha, b, c, d: anb = 0, ac = 1, db = 1, dc = 1, dab = 1, da 2 b = 1,.., dan-1 b = 1i are congruence-free for all n = 1. This provides a new countable family of finitely presented congruence-free monoids, bringing us one step closer to understanding the monoid version of the Boone-Higman Conjecture. We also provide examples showing that finitely presented congruence-free monoids may have quadratic Dehn function.
KW - Boone-Higman Conjecture
KW - Congruence-free
KW - Finitely presented
KW - Rewriting systems
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U2 - 10.14232/actasm-013-028-z
DO - 10.14232/actasm-013-028-z
M3 - Article
AN - SCOPUS:84953876715
SN - 0001-6969
VL - 81
SP - 437
EP - 445
JO - Acta Scientiarum Mathematicarum
JF - Acta Scientiarum Mathematicarum
IS - 3-4
ER -