On balanced order relations and the normal hull of completely simple semirings

Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 1

Abstract

In [1] the authors proved that a semiring S is a completely simple semiring if and only if S is isomorphic to a Rees matrix semiring over a skew-ring R with sandwich matrix P and index sets I and Λ which are bands under multiplication. In this paper we characterize all the balanced order relations on completely simple semirings. Also we study the normal hull of a completely simple semiring. Keywords: skew-ring, Rees matrix semiring, balanced order relation, essential extension, normal extension, normal ideal, normal hull. 2010 Mathematics Subject Classification: 16A78, 20M07, 20M10.

Authors and Affiliations

Sunil Maity

Keywords

Related Articles

ON L-FUZZY MULTIPLICATION MODULES

Let L be a complete lattice. In a manner analogous to a commutative ring, we introduce and investigate the L-fuzzy multiplication modules over a commutative ring with non-zero identity. The basic properties of the prime...

An ideal-based zero-divisor graph of direct products of commutative rings

In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings....

ON QI-ALGEBRAS

In this paper, the notion of a QI-algebra is introduced which is a generalization of a BI-algebra and there are studied its properties. We considered ideals, congruence kernels in a QI-algebra and characterized congruenc...

Characterizations of ordered Γ-Abel-Grassmann's groupoids

In this paper, we introduced the concept of ordered Γ-AG-groupoids, Γ- ideals and some classes in ordered Γ-AG-groupoids. We have shown that every Γ-ideal in an ordered Γ-AG∗∗-groupoid S is Γ-prime if and only if it is Γ...

Intervals of certain classes of Z-matrices

Let A and B be M-matrices satisfying A ≤ B and J = [A, B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible Mmatr...

Download PDF file
  • EP ID EP165173
  • DOI -
  • Views 37
  • Downloads 0

How To Cite

Sunil Maity (2014). On balanced order relations and the normal hull of completely simple semirings. Discussiones Mathematicae - General Algebra and Applications, 34(1), -. https://europub.co.uk/articles/-A-165173