FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 1, PAGES 223-232

**Regular $S$-acts with primitive normal and
antiadditive theories**

A. A. Stepanova

G. I. Baturin

Abstract

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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 $$_{S}R is
a maximal (under the inclusion) regular subact of the $S$-act $$_{S}S.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k111/k11113h.htm

Last modified: January 31, 2012