Related papers: On the embedding of Gamma-semigroup amalgam
The concept of $\Gamma$-semigroups was introduced by M. K Sen in 1981. This study aims to investigate several intriguing properties of $\Gamma$-semigroups and to provide the concepts of simple $\Gamma$-semigroups, 0-simple…
The concept of a $\Gamma$-semigroup has been introduced by Mridul Kanti Sen in the Int. Symp., New Delhi, 1981. It is well known that the Green's relations play an essential role in studying the structure of semigroups. In the present paper…
Our aim is to show the way we pass from the results of ordered semigroups (or semigroups) to ordered $\Gamma$-semigroups (or $\Gamma$-semigroups). The results of this note have been transferred from ordered semigroups. The concept of…
Given a $\Gamma$-semigroup $S$, we construct a semigroup $\Sigma$ in such a way that one sided ideals and quasi-ideals of $S$ can be regarded as one sided ideals and quasi-ideals respectively of $\Sigma$. This correspondence and other…
A semigroup amalgam (S; T1, T2) is known to be non-embeddable if T1 and T2 are both groups (completely regular semigroups, Clifford semigroups) but S is not such. We prove some non-embeddability conditions for semigroup amalgams (S; T1, T2)…
The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
In this paper, the definitions of soft {\Gamma}-semirings and soft sub {\Gamma}-semi rings are introduced with the aid of the concept of soft set theory introduced by Molodtsov. In the mean time, some of their properties and structural…
We add here some further characterizations to the characterizations of strongly regular ordered $\Gamma$-semigroups already considered in Hacettepe J. Math. 42 (2013), 559--567. Our results generalize the characterizations of strongly…
In this paper the concept of Q-fuzzification of ideals of gamma-semigroups has been introduced and some important properties have been investigated. A characterization of regular gamma-semigroup in terms of Q-fuzzy ideals has been obtained.…
The notion of $\Gamma$-semirings was introduced by Murali Krishna Rao \cite{Rao} as a generalization of the notion of $\Gamma$-rings as well as of semirings. We have known that the notion of $\Gamma$-semirings is a generalization of the…
Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and…
In the present paper we study locally semiflat (we also call them semiintegrable) almost Grassmann structures. We establish necessary and sufficient conditions for an almost Grassmann structure to be alpha- or beta-semiintegrable. These…
The problem of embedding an ample semigroup in an inverse semigroup as a (2, 1, 1)-type subalgebra is known to be undecidable. In this article, we investigate the problem for certain classes of ample semigroups. We also give examples of…
Let $\Gamma$ be a totally ordered group. We use Hahn's embedding theorem to construct a totally ordered set $\Gamma\subset \Gamma_{\operatorname{sme}}$ which classifies small extensions of $\Gamma$. This small-extensions closure…
Suppose we wish to embed an (associative) $k$-algebra $A$ in a $k$-algebra $R$ generated in some specified way; e.g., by two elements, or by copies of given $k$-algebras $A_1,$ $A_2,$ $A_3.$ Several authors have obtained sufficient…
Let $S$ be a semigroup, $\Lambda$ a non-empty set and $P$ a mapping of $\Lambda$ into $S$. The set $S\times \Lambda$ together with the operation $\circ _P$ defined by $(s, \lambda)\circ _P(t, \mu )=(sP(\lambda)t, \mu )$ form a semigroup…
This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.
Let $\Gamma$ be a finitely generated group which is hyperbolic relative to a finite family $\{H_1,...,H_n\}$ of subgroups. We prove that $\Gamma$ is uniformly embeddable in a Hilbert space if and only if each subgroup $H_i$ is uniformly…
For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].