The purpose of this paper is to determine some forms of the relations m a finite semigroup presentation with zero deficiency which have solvable word problem via Adian graphs.
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 ...
In this paper, Gro¨ bner–Shirshov bases (noncommutative) for extended modular, ex
tended Hecke and Picard groups are considered. A new algorithm for obtaining normal forms of
elements and hence solving the word problem ...
Ateş, Fırat; Karpuz, Eylem G.; Çevik, Sinan(American Institute of Physics, 2011)
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.
Çevik, A. Sinan; Karpuz, Eylem G.; Ateş, Fırat(American Institute of Physics, 2011)
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 ...
In this paper we give a partial answer to the problem which is about the regularity of Schützenberger product in semigroups asked by Gallagher in his thesis [4, Problem 6.1.6]. Furthermore, we determine necessary and ...
Karpuz, Eylem Güzel; Çevik, Ahmet Sinan; Koppitz, Jörg; Cangül, İsmail Naci(Springer, 2013)
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 π-inverse. These semigroup classes ...
Karpuz, Eylem Güzel; Das, Kinkar Chandra; Cangül, İsmail Naci; Çevik, Ahmet Sinan(Springer, 2013)
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, ...
Let us consider groups G1 = Zk ∗ (Zm ∗ Zn), G2 = Zk ×(Zm ∗ Zn), G3 = Zk ∗ (Zm ×Zn),
G4 = (Zk ∗ Zl) ∗ (Zm ∗ Zn) and G5 = (Zk ∗ Zl)×(Zm ∗ Zn), where k, l,m, n ≥ 2. In this
paper, by defining a new graph (Gi) based on the ...
Karpuz, E. Güzel; Ateş, Fırat; Çevik, A. Sinan; Cangül, İ. Naci; Maden Güngör, A. Dilek(Elsevier, 2011)
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 ...
The main goal of this paper is to define Gröbner–Shirshov bases for some monoids.
Therefore, after giving some preliminary material, we first give Gröbner–Shirshov bases for
graphs and Schützenberger products of monoids ...
In this paper, torsion-free part of U1(ZCs) is characterized by using a different description. That is, unlike the previous works, a classical ring and number theory is used in this characterization.
It is known that linear matrix equations have been one of the main topics in matrix theory
and its applications. The primary work in the investigation of a matrix equation (system) is
to give solvability conditions and ...
Some complex quaternionic equations in the type AX-XB= C are investigated. For convenience, these equations were called
generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. ...
In this paper, we establish several new connections between the generalizations of Fibonacci
and Lucas sequences and Hessenberg determinants. We also give an interesting conjecture
related to the determinant of an infinite ...
The main concerns of this paper are the linear equations with one term and one unknown of the forms: a(xa) =r, a(xb ) =
r and (ax)b =r, and the linear equations with two terms and one unknown of the forms: (ax)b +(g x)d ...
Abdioĝlu, C.; Koşan, M.T.; Şahinkaya, S.(Southeast Asian Bulletin of Mathematics, 2010)
The notion of projection invariant subgroups was first introduced by Fuchs in
[7]. We will define the module-theoretic version of the projection invariant subgroup.
Let R be a ring and M a right R-module. We call a ...
Let R be a commutative Noetherian ring with non-zero identity and a
an ideal of R. In the present paper, we examine the question whether the support of
Hn
a (N;M) must be closed in Zariski topology, where Hn
a (N;M) ...