Congruence-simple semirings without nilpotent elements
Tom\'a\v{s} Kepka, Miroslav Korbel\'a\v{r}, G\"unter Landsmann
TL;DR
This paper classifies a specific class of semirings that are simple with respect to congruences, contain an absorbing element, and lack non-trivial nilpotent elements, advancing understanding in algebraic structures.
Contribution
It offers a complete classification of congruence-simple semirings with an absorbing element and no non-trivial nilpotent elements, a previously uncharacterized class.
Findings
Classification of congruence-simple semirings achieved
Identification of conditions for semirings with absorbing elements
Clarification of the structure of nilpotent-free semirings
Abstract
We provide a classification of congruence-simple semirings with a multiplicatively absorbing element and without non-trivial nilpotent elements.
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