The next step of the word problem over monoids
APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.794-798, 2011 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 218 Issue: 3
- Publication Date: 2011
- Doi Number: 10.1016/j.amc.2011.03.076
- Journal Name: APPLIED MATHEMATICS AND COMPUTATION
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.794-798
- Bursa Uludag University Affiliated: Yes
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. (C) 2011 Elsevier Inc. All rights reserved.