Geodesic
Polygons with primitive normal and additive theories
Algebra i logika, Tome 47 (2008) no. 4, pp. 491-508.

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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.
Mots-clés : polygon
Keywords: primitive normal theory, additive theory, antiadditive theory. 
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A. A. Stepanova. Polygons with primitive normal and additive theories. Algebra i logika, Tome 47 (2008) no. 4, pp. 491-508. http://geodesic.mathdoc.fr/item/AL_2008_47_4_a5/

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