FDT FOR Ω-MONOIDS
Keywords:
-semigroup, FDT, string-rewriting systems, derivation graph, homotopy
Abstract
In this paper we generalize the results of C.Squier ([1]) in the case of -monoids. We give, first,
the definition of -semigroups and some general results related to the -string rewriting
systems, the properties of confluence, termination, Church-Rosser, and so on. Finally, we prove
our main theorem which states that if is a finitely presented -monoid which has a
presentation involving a finite convergent -string rewriting system , then has finite
derivation type.
References
1. C.C.Squier, F.Otto,Y.Kobayashi, (1994), A finiteness condition for rewriting systems,
Theoretical Computer Science,131, 271-294.
2. C.Squier, (1987), Word problems and a homological finiteness condition for monoids,
Journal of Pure and Applied Algebra 49, 201-217.
3. C.Squier, F.Otto, (1987), The word problem for finitely presented monoids and finite
canonical rewriting systems.
4. Y.Lafont, (2006), Algebra and Geometry of Rewriting.
5. R.V.Book, F.Otto, (1993), String-Rewriting Systems, Springer-Verlag,New York.
6. P.A. Grillet, (2007), Abstract Algebra, 2nd edition, Springer.. E.Pasku, (2006),
7. Finiteness Conditions for Monoids and Small Categories, PhD Thesis,
18-23.
Theoretical Computer Science,131, 271-294.
2. C.Squier, (1987), Word problems and a homological finiteness condition for monoids,
Journal of Pure and Applied Algebra 49, 201-217.
3. C.Squier, F.Otto, (1987), The word problem for finitely presented monoids and finite
canonical rewriting systems.
4. Y.Lafont, (2006), Algebra and Geometry of Rewriting.
5. R.V.Book, F.Otto, (1993), String-Rewriting Systems, Springer-Verlag,New York.
6. P.A. Grillet, (2007), Abstract Algebra, 2nd edition, Springer.. E.Pasku, (2006),
7. Finiteness Conditions for Monoids and Small Categories, PhD Thesis,
18-23.
Published
2018-11-30
Section
Articles
- All contributor(s) agree to transfer the copyright of this article to IOJPH Journal.
- IOJPH Journal will have all the rights to distribute, share, sell, modify this research article with proper reference of the contributors.
- IOJPH Journal will have the right to edit or completely remove the published article on any misconduct happening.
