Geodesic
Primitive normality and primitive connectedness of the class of injective $S$-acts
Algebra i logika, Tome 59 (2020) no. 2, pp. 155-168

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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.
Keywords: monoid, $S$-act, injective $S$-act, primitive normal theory, primitive connected theory. 
@article{AL_2020_59_2_a0,
     author = {E. L. Efremov},
     title = {Primitive normality and primitive connectedness of the class of injective $S$-acts},
     journal = {Algebra i logika},
     pages = {155--168},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_2_a0/}
}
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E. L. Efremov. Primitive normality and primitive connectedness of the class of injective $S$-acts. Algebra i logika, Tome 59 (2020) no. 2, pp. 155-168. http://geodesic.mathdoc.fr/item/AL_2020_59_2_a0/