Abstract
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 of a semigroup R such that an S-act sR is a maximal (under the inclusion) regular subact of the S-act sS.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 1, pp. 223–232, 2011/12.
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Stepanova, A.A., Baturin, G.I. Regular S-acts with primitive normal and antiadditive theories. J Math Sci 185, 497–503 (2012). https://doi.org/10.1007/s10958-012-0931-z
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DOI: https://doi.org/10.1007/s10958-012-0931-z