Related papers: On ordered $\Gamma$-semigroups ($\Gamma$-semigroup…
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…
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…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
The aim is to correct part of the Remark 3 of my paper "On regular, intra-regular ordered semigroups" in Pure Math. Appl. (PU.M.A.) 4, no. 4 (1993), 447--461. On this occasion, some further results and the similarity between the…
This is about the paper in the title by Kostaq Hila in Rocky Mt. J. Math. 41, no. 1 (2011), 189-203 for which corrections should be done.
This is about the paper in the title published by K. Hila and J. Dine in Acta Math. Sinica, English Series, 29, no. 3, (2013), 609--624.
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…
The purpose of this paper is to study the generalization of inverse semigroups (without order). An ordered semigroup S is called an inverse ordered semigroup if for every a 2 S, any two inverses of a are H-related. We prove that an ordered…
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…
In this short note, we show that the generalized type semigroup $\CW(X, \Gamma)$ introduced by the author in \cite{M3} belongs to the category \textnormal{W}. In particular, we demonstrate that $\CW(X, \Gamma)$ satisfies axioms (W1)-(W4)…
We characterize the intra-regular $\Gamma$-semigroups and the left regular $\Gamma$-semigroups $M$ in which $x\Gamma M\subseteq M\Gamma x$ for every $x\in M$ in terms of filters and we prove, among others, that every intra-regular…
We keep the definition of intra-regularity (left regularity) of $po$-$\Gamma$-semigroups introduced in arXiv: 1511.00679 which is absolutely necessary for the investigation. Being able to describe the form of the elements of the principal…
Rational semigroups were introduced by Hinkkanen and Martin as a generalization of the iteration of a single rational map. There has subsequently been much interest in the study of rational semigroups. Quasiregular semigroups were…
Lee and Kwon [12] defined an ordered semigroup S to be completely regular if a 2 (a2Sa2] for every a 2 S. We characterize every completely regular ordered semigroup as a union of t-simple subsemigroups, and every Clifford ordered semigroup…
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…
Gamma-semigroup is introduced as a generalization of semigroups by M. K Sen and Saha. In this paper we describe amalgam of two Gamma-semigroups and discuss the embeddability of this amalgam. Further we obtained a necessary condition for the…
A semigroup together with compatible partial order is called an odered semigroup. In this paper we discuss the ordered matrix semigroups.
This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.
In this article, we give a complete characterization of semigroup graded rings which are graded von Neumann regular. We also demonstrate our results by applying them to several classes of examples, including matrix rings and groupoid graded…
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…