The next step of the word problem over monoids
Date
2011-10
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Science
Abstract
It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spherical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable "generalized identity problem'' that can be thought as the next step (or one-dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications.
Description
Keywords
Mathematics, Monoid pictures, Word problem, Presentation, Identity problem, Homological finiteness condition, Group presentation, Identity problem, Monoid pictures, Monoids, One-dimension, Physical application, Presentation, Word problem, Algebra
Citation
Karpuz, E. G. vd. (2011). "The next step of the word problem over monoids". Applied Mathematics and Computation, 218(3), 794-798.