Classification of nonsemicommutative rings

The classes of semicommutative, PS I, 2-primal, weakly-2-primal, NI, NR and Dedekind-finite rings form a strictly increasing chain of classes of rings. Examples have been provided by several authors to show most of the inclusions are strict. In this paper it is shown that every inclusion is strict....

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Bibliographic Details
Published in:Acta mathematica Hungarica 2021-10, Vol.165 (1), p.48-62
Main Authors: Chimal-Dzul, H., Szabo, S.
Format: Article
Language:English
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Summary:The classes of semicommutative, PS I, 2-primal, weakly-2-primal, NI, NR and Dedekind-finite rings form a strictly increasing chain of classes of rings. Examples have been provided by several authors to show most of the inclusions are strict. In this paper it is shown that every inclusion is strict. Furthermore, in most instances examples with the additional properties of being reflexive and/or abelian are constructed. In particular, an abelian nonreflexive NI non-weakly-2-primal ring is given, which shows that the classes of NI and weakly-2-primal rings differ; a fact that has been previously claimed without proof.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-021-01165-3