B-lattice of nil-extensions of rectangular skew-rings

TL;DR

This paper investigates a specific class of semirings called b-lattices of nil-extensions of orthodox completely simple semirings, expanding the understanding of their algebraic structure.

Contribution

It introduces and analyzes the structure of b-lattices of nil-extensions of orthodox completely simple semirings, a specific subclass within semiring theory.

Findings

Characterization of b-lattices of nil-extensions of orthodox completely simple semirings

Extension of known results from quasi completely regular semirings

New insights into the algebraic structure of these semirings

Abstract

Every quasi completely regular semiring is a b-lattice of completely Archimedean semirings, i.e., a b-lattice of nil-extensions of completely simple semirings. In this paper we consider the semiring which is a b-lattice of nil-extensions of orthodox completely simple semirings.