TL;DR
This paper investigates specific classes of ringoids, focusing on their simplicity properties and exploring structures like generalized parasemifields and non-associative semirings to understand their algebraic characteristics.
Contribution
It introduces and analyzes congruence-simple and ideal-simple classes of ringoids, expanding understanding of their structure and properties, especially in the context of generalized parasemifields and non-associative semirings.
Findings
Characterization of congruence-simple ringoids
Analysis of ideal-simple ringoids
Insights into non-associative semiring structures
Abstract
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particular, we examine generalised parasemifields and non-associative semirings.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory