Geodesic
Regular $S$-acts with primitive normal and antiadditive theories
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 1, pp. 223-232

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In this work, we investigate the commutative monoids over which the axiomatizable class of regular $S$-acts is primitive normal and antiadditive. We prove that the primitive normality of an axiomatizable class of regular $S$-acts over the commutative monoid $S$ is equivalent to the antiadditivity of this class and it is equivalent to the linearity of the order on a semigroup $R$ such that an $S$-act $_SR$ is a maximal (under the inclusion) regular subact of the $S$-act $_SS$. 
@article{FPM_2012_17_1_a12,
     author = {A. A. Stepanova and G. I. Baturin},
     title = {Regular $S$-acts with primitive normal and antiadditive theories},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {223--232},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_1_a12/}
}
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A. A. Stepanova; G. I. Baturin. Regular $S$-acts with primitive normal and antiadditive theories. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 1, pp. 223-232. http://geodesic.mathdoc.fr/item/FPM_2012_17_1_a12/