The next step of the word problem over monoids

Karpuz E. G., ATEŞ F., ÇEVİK A. S., CANGÜL İ. N., Maden (Gungor) A. D.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.794-798, 2011 (SCI-Expanded) identifier identifier

  • 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.