Primitive Normality and Primitive Connectedness of the Class of Injective S-Acts

The paper deals monoids over which the class of all injective S -acts is primitive normal and primitive connected. The following results are proved: the class of all injective acts over any monoid is primitive normal; the class of all injective acts over a right reversible monoid S is primitive conn...

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Bibliographic Details
Published in:Algebra and logic 2020-05, Vol.59 (2), p.103-113
Main Author: Efremov, E. L.
Format: Article
Language:English
Subjects:
Algebra
Group theory
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
Monoids
Normality
Theorems (Mathematics)
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Summary:The paper deals monoids over which the class of all injective S -acts is primitive normal and primitive connected. The following results are proved: the class of all injective acts over any monoid is primitive normal; the class of all injective acts over a right reversible monoid S is primitive connected iff S is a group; if a monoid S is not a group and the class of all injective acts is primitive connected, then a maximal (w.r.t. inclusion) proper subact of S S is not finitely generated.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-020-09584-x