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

View as HTML     View as gif image

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.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k111/k11113h.htm
Last modified: January 31, 2012