Karpuz, Eylem GüzelAteş, FıratÇevik, Ahmet SinanMaden, Ayşe Dilek Güngör2022-03-302022-03-302011-10Karpuz, E. G. vd. (2011). "The next step of the word problem over monoids". Applied Mathematics and Computation, 218(3), 794-798.0096-30031873-5649https://doi.org/10.1016/j.amc.2011.03.076https://www.sciencedirect.com/science/article/pii/S0096300311004449http://hdl.handle.net/11452/25419It 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.eninfo:eu-repo/semantics/openAccessMathematicsMonoid picturesWord problemPresentationIdentity problemHomological finiteness conditionGroup presentationIdentity problemMonoid picturesMonoidsOne-dimensionPhysical applicationPresentationWord problemAlgebraArticle0002942984000302-s2.0-800522697407947982183Mathematics, appliedMonoids; Inverse Semigroup; Word Problem