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
AGGREGATING FUZZY BINARY RELATIONS AND FUZZY FILTERS
The main goal of this paper is to investigate the aggregation of diverse families of binary fuzzy relations, fuzzy filters, and fuzzy lattices. Some links between these families and their images via an aggregation are ex...
All Maximal Completely Regular Submonoids of HypG(2)
In this paper we consider mappings σ which map the binary operation symbol f to the term σ(f) which do not necessarily preserve the arity. These mapping are called generalized hypersubstitutions of type τ = (2) and we de...
QUASIORDER LATTICES ARE FIVE-GENERATED
transitive relation. The quasiorders on a set A form a complete lattice with respect to set inclusion. Assume that A is a set such that there is no inaccessible cardinal less than or equal to |A|; note that in Kuratowski...
Generalized derivations in prime rings and Banach algebras
Let R be a prime ring with extended centroid C, F a generalized derivation of R and n ≥ 1, m ≥ 1 fixed integers. In this paper we study the situations: 1. (F(x ◦ y))m = (x ◦ y) n for all x, y ∈ I, where I is a nonzero id...
Bi-Interior Ideals of Semigroups
In this paper, as a further generalization of ideals, we introduce the notion of bi-interior ideal as a generalization of quasi ideal, bi-ideal and interior ideal of semigroup and study the properties of bi-interior idea...