Some Decision Problems for Extended Modular Groups

In this paper we investigate solvability of the word problem for Extended Modular groups, Extended Hecke groups and Picard groups in terms of complete rewriting systems. At the final part of the paper we examine the other important decision problem (conjugacy problem) for only Extended Modular groups

The Efficiency of the Semi-Direct Products of Free Abelian Monoid with Rank n by the Infinite Cyclic Monoid

In this paper we give necessary and sufficient conditions for the efficiency of the semi-direct product of free abelian monoid with rank n by the infinite cyclic monoid

Conjugacy for Free Groups under Split Extensions

At the present paper we show that conjugacy is preserved and reflected by the natural homomorphism defined from a semigroup S to a group G, where G defines split extensions of some free groups. The main idea in the proofs is based on a geometrical structure as applied in the paper [8]

Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids

This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then construct biautomatic structures. For hypoplactic monoids, we construct finite complete rewriting systems and biautomatic structures. For sylvester monoids, which are not finitely presented, we prove that the standard presentation is an infinite complete rewriting system, and construct biautomatic structures. Consequently, the monoid algebras corresponding to monoids of these classes are automaton algebras in the sense of Ufnarovskij

A new graph based on the semi-direct product of some monoids

In this paper, firstly, we define a new graph based on the semi-direct product of a free abelian monoid of rank n by a finite cyclic monoid, and then discuss some graph properties on this new graph, namely diameter, maximum and minimum degrees, girth, degree sequence and irregularity index, domination number, chromatic number, clique number of (PM). Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in fields such as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics

Finite derivation type for graph products of monoids

Bu çalışma, 08-11, Ağustos 2014 tarihlerinde Gyeongju[Güney Kore]’de düzenlenen 22. International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (ICFIDCAA) Kongresi‘nde bildiri olarak sunulmuştur.The aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.Balıkesir Üniversitesi - 2014/95, 2015/4

Some fixed-point results on (generalized) Bruck-Reilly-extensions of monoids

In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly *-extensions of arbitrary monoids to be regular, coregular and strongly pi-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.Selçuk Üniversitesi (13701071

The next step of the word problem over monoids

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 spher- ical 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