Abstract
We present a purely combinatorial approach to the question of whether or not a finitely presented monoid has a finite canonical presentation. Our approach is based on the notion of “finite derivation type” which is a combinatorial condition satisfied by certain rewriting systems. Our main result states that if a monoid M has a finite canonical presentation, then all finite presentations of M have finite derivation type. By proving that a certain monoid S 1 does not have finite derivation type we show in addition that the homological finiteness condition FP ∞ is not sufficient to guarantee that a finitely presented monoid with a decidable word problem has a finite canonical presentation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
