Some Structures of Hemirings

Md Yasin Ali

doi:10.11648/j.pamj.20170601.16

Abstract

Hemirings appear in a natural manner, in some applications to the theory of automata, the theory of formal languages, graph theory, design theory and combinatorial geometry. Recently, the notions of hemirings with special structures were introduced. But still now there are no complete structural properties of hemirings. In this paper we try to investigate some structures of hemirings. This is done by introducing some examples of hemirings.

Highlights

Hemirings which are regarded as a generalization of rings have been found useful in solving problems in different areas of applied mathematics and computer sciences [2, 3, 5]
Golan [1] quoted some special classes of hemirings such as idempotent hemiring, zerosumfree hemiring, regular hemiring and so on
In this paper we characterized some classes of hemirings especially zerosumfree hemiring, idempotent hemiring, regular hemiring and simple hemiring counter examples are given

Summary

Introduction

Hemirings which are regarded as a generalization of rings have been found useful in solving problems in different areas of applied mathematics and computer sciences [2, 3, 5]. Golan [1] quoted some special classes of hemirings such as idempotent hemiring, zerosumfree hemiring, regular hemiring and so on. M. Gulistan et al [7] characterize the gamma hemirings through level cuts in terms of generalized fuzzy (left, right, prime, semiprime) gamma ideals of gamma hemirings. Yin et al [10] gave the notions of h -semisimple hemirings and invested the characterizations by fuzzy ideals. Some researches on hemirings are focused on fuzzy ideals [6, 12, 14,15,16], soft set theory [11] and bipolar fuzzy theory [17]. In this paper we characterized some classes of hemirings especially zerosumfree hemiring, idempotent hemiring, regular hemiring and simple hemiring counter examples are given. This paper is organized as follows: in section 2 we describe some preliminaries on hemirings, in section 3 some structures on hemirings are given, in section 4 the structures of simple hemirings are described

Preliminaries

Some Structures of Hemirings

Structure of Simple Hemirings

Conclusion