The Primitive Normality of a Class of Weakly Injective S-Acts

The notion of weakly injective -act can be regarded as a generalization of the notion of injective -act. This article describes the finite monoids over which each weakly injective -act has a primitively normal theory. Moreover, we show that the primitive normality of the class of all principally wea...

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Bibliographic Details
Published in:Siberian mathematical journal 2021-05, Vol.62 (3), p.521-536
Main Authors: Stepanova, A. A., Efremov, E. L.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Monoids
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Summary:The notion of weakly injective -act can be regarded as a generalization of the notion of injective -act. This article describes the finite monoids over which each weakly injective -act has a primitively normal theory. Moreover, we show that the primitive normality of the class of all principally weakly injective -acts is equivalent to  being totally ordered.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446621030150