Abstract
Squier [10] considered homotopy relations on the paths of the derivation graphs associated with monoid presentations in connection with the word problem. He introduced the notion of FDT (finite derivation type), which is a certain finiteness condition on homotopy of monoid presentations. He proved that FDT is an intrinsic property of a monoid not depending on its presentation. Moreover he proved that if a monoid admits a finite complete presentation, then it has FDT, and thus he could prove that his monoid S1 with solvable word problem has no finite complete presentation by showing that it does not have FDT.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Cremanns and F. Otto, Finite derivation type implies the homological finiteness condition FP3, J. Symbolic Comput., 18 (1994), 91–112.
R. Cremanns and F. Otto, For groups the property of finite derivation type is equivalent to the homological finiteness condition FP3,J. Symbolic Comput., 22 (1996), 155–177.
N. Dershowitz and Z. Manna, Proving termination with multiset orderings, Comm. Assoc. Comput. Mach., 22 (1979), 465–476.
V. Guba and M. Sapir, Diagram Groups, Mem. Amer. Math. Soc. 620, vol. 130, American Mathematical Society, Providence, 1997.
Y. Kobayashi, Complete rewriting systems and the homology of monoid algebras, J. PureAppl. Algebra, 65 (1990), 321–329.
Y. Kobayashi, Homotopy reduction systems for monoid presentations: Asphericity and low-dimensional homology, J. Pure Appl. Algebra, 130 (1998), 159–195.
Y. Lafont, A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier), J. PureAppl. Algebra, 98 (1995), 229–244.
S.J. Pride, Low-dimensional homotopy theory for monoids, Intern. J. Algebra Comput., 5 (1995), 631–649.
S.J. Pride, Low-dimensional homotopy theory for monoids II: Groups, Glasgow Math. J., to appear.
C.C. Squier, F. Otto, and Y. Kobayashi, A finiteness condition for rewriting systems, Theoret. Comput. Sci., 131 (1994), 271–294.
X. Wang and S.J. Pride, Second order Dehn functions of groups and monoids, preprint.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this paper
Cite this paper
Kobayashi, Y. (2000). Homotopy Reduction Systems for Monoid Presentations II: The Guba—Sapir Reduction and Homotopy Modules. In: Birget, JC., Margolis, S., Meakin, J., Sapir, M. (eds) Algorithmic Problems in Groups and Semigroups. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1388-8_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1388-8_8
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7126-0
Online ISBN: 978-1-4612-1388-8
eBook Packages: Springer Book Archive