Commutators in Semirings

We provide a characterization of abelian and nilpotent semirings with absorbing zero as well as a characterizations of solvability in additively cancellative semirings with absorbing zero. In semirings with absorbing zero, supernilpotency implies nilpotency.

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: Mudrinski, Nebojša, Šobot, Milica
Format: Article
Language:English
Subjects:
Commutators
Rings (mathematics)
Online Access:Get full text
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Description
Summary:We provide a characterization of abelian and nilpotent semirings with absorbing zero as well as a characterizations of solvability in additively cancellative semirings with absorbing zero. In semirings with absorbing zero, supernilpotency implies nilpotency.
ISSN:2331-8422