2018/04/25 by Stepanova, A. A., Baturin, G. I.
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1804.09353
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.