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

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Algebra and Logic Aims and scope

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 SS is not finitely generated.

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Authors and Affiliations

  1. Far Eastern Federal University, ul. Sukhanova 8, Vladivostok, 690091, Russia

    E. L. Efremov

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  1. E. L. Efremov
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Correspondence to E. L. Efremov.

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(E. L. Efremov) Supported by RFBR (project No. 17-01-00531) and by RF Ministry of Education and Science (Suppl. Agreement No. 075-02-2020-1482-1 of 21.04.2020).

Translated from Algebra i Logika, Vol. 59, No. 2, pp. 155-168, March-April, 2020.

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Efremov, E.L. Primitive Normality and Primitive Connectedness of the Class of Injective S-Acts. Algebra Logic 59, 103–113 (2020). https://doi.org/10.1007/s10469-020-09584-x

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  • DOI: https://doi.org/10.1007/s10469-020-09584-x

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