Geodesic
Primitive Connected and Additive Theories of Polygons
Algebra i logika, Tome 45 (2006) no. 3, pp. 300-313

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We study into monoids $S$ the class of all $S$-polygons over which is primitive normal, primitive connected, or additive, that is, the monoids $S$ the theory of any $S$-polygon over which is primitive normal, primitive connected, or additive. It is proved that the class of all $S$-polygons is primitive normal iff $S$ is a linearly ordered monoid, and that it is primitive connected iff $S$ is a group. It is pointed out that there exists no monoid $S$ with an additive class of all $S$-polygons.
Keywords: primitive connected theory, additive theory
Mots-clés : polygon. 
@article{AL_2006_45_3_a1,
     author = {A. A. Stepanova},
     title = {Primitive {Connected} and {Additive} {Theories} of {Polygons}},
     journal = {Algebra i logika},
     pages = {300--313},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_3_a1/}
}
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A. A. Stepanova. Primitive Connected and Additive Theories of Polygons. Algebra i logika, Tome 45 (2006) no. 3, pp. 300-313. http://geodesic.mathdoc.fr/item/AL_2006_45_3_a1/