Centrally Essential Semirings
Oleg Lyubimtsev, Askar Tuganbaev
TL;DR
This paper introduces the concept of centrally essential semirings, explores their properties, and provides examples, especially focusing on non-commutative cases and additively cancellative structures.
Contribution
It defines centrally essential semirings, offers examples of non-commutative instances, and investigates properties of additively cancellative centrally essential semirings.
Findings
Examples of non-commutative centrally essential semirings
Characterization of properties of additively cancellative centrally essential semirings
Insights into the structure of centrally essential semirings
Abstract
A semiring is said to be centrally essential if for every non-zero element , there exist two non-zero central elements with . We give some examples of non-commutative centrally essential semirings and describe some properties of additively cancellative centrally essential semirings.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Fuzzy and Soft Set Theory