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Algebra Logika, 2008, Volume 47, Number 4, Pages 491–508 (Mi al370)  

This article is cited in 5 scientific papers (total in 5 papers)

Polygons with primitive normal and additive theories

A. A. Stepanova


Abstract: Previously, primitive normal, primitive connected, and additive theories of $S$-polygons were studied. In particular, it was proved that the class of all $S$-polygons is primitive normal iff $S$ is a linearly ordered monoid. The present paper is a continuation of this research. Here, Spolygons with primitive normal, additive, and antiadditive theories are described in the language of a primitive equivalence structure. It is shown that the class of all $S$-polygons is antiadditive only for a linearly ordered monoid $S$, that is, this class is antiadditive iff it is primitive normal.

Keywords: polygon, primitive normal theory, additive theory, antiadditive theory.

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English version:
Algebra and Logic, 2008, 47:4, 279–288

Bibliographic databases:

UDC: 510.67+512.56
Received: 28.04.2007

Citation: A. A. Stepanova, “Polygons with primitive normal and additive theories”, Algebra Logika, 47:4 (2008), 491–508; Algebra and Logic, 47:4 (2008), 279–288

Citation in format AMSBIB
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\by A.~A.~Stepanova
\paper Polygons with primitive normal and additive theories
\jour Algebra Logika
\yr 2008
\vol 47
\issue 4
\pages 491--508
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\transl
\jour Algebra and Logic
\yr 2008
\vol 47
\issue 4
\pages 279--288
\crossref{https://doi.org/10.1007/s10469-008-9019-8}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Stepanova, G. I. Baturin, “Regular $S$-acts with primitive normal and antiadditive theories”, J. Math. Sci., 185:3 (2012), 497–503  mathnet  crossref
    2. D. O. Ptakhov, “Primitive normality and additivity of free projective and strongly flat polygons”, Algebra and Logic, 53:5 (2014), 397–404  mathnet  crossref  mathscinet  isi
    3. A. A. Stepanova, A. I. Krasitskaya, “Primitive normality and primitive connectedness of a class of divisible polygons”, Algebra and Logic, 58:5 (2019), 434–440  mathnet  crossref  crossref  isi
    4. E. L. Efremov, “Primitive normality and primitive connectedness of the class of injective $S$-acts”, Algebra and Logic, 59:2 (2020), 103–113  mathnet  crossref  crossref  isi
    5. A. A. Stepanova, E. L. Efremov, “Primitivnaya normalnost klassa slabo in'ektivnykh poligonov”, Sib. matem. zhurn., 62:3 (2021), 640–658  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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