Journal of Mathematical Sciences

, Volume 185, Issue 3, pp 497–503 | Cite as

Regular S-acts with primitive normal and antiadditive theories



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.


Binary Operation Atomic Formula Regular Polygon Commutative Monoid Additive Theory 
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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceFar East State UniversityVladivostokRussia

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