Primitive normality and additivity of free projective and strongly flat polygons
Algebra i logika, Tome 53 (2014) no. 5, pp. 614-624.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study into monoids $S$ over which the axiomatizable class of all free, projective, or strongly flat $S$-polygons is primitive normal or additive. It is proved that an axiomatizable class of all free, projective, or strongly flat $S$-polygons is primitive normal iff a monoid$S$ primitive normal. Also it is shown that an axiomatizable class of all free, projective, or strongly flat $S$-polygons is not additive for any monoid $S$.
Keywords: primitive normal theory, additive theory
Mots-clés : polygon.
@article{AL_2014_53_5_a3,
     author = {D. O. Ptakhov},
     title = {Primitive normality and additivity of free projective and strongly flat polygons},
     journal = {Algebra i logika},
     pages = {614--624},
     publisher = {mathdoc},
     volume = {53},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2014_53_5_a3/}
}
TY  - JOUR
AU  - D. O. Ptakhov
TI  - Primitive normality and additivity of free projective and strongly flat polygons
JO  - Algebra i logika
PY  - 2014
SP  - 614
EP  - 624
VL  - 53
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2014_53_5_a3/
LA  - ru
ID  - AL_2014_53_5_a3
ER  - 
%0 Journal Article
%A D. O. Ptakhov
%T Primitive normality and additivity of free projective and strongly flat polygons
%J Algebra i logika
%D 2014
%P 614-624
%V 53
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2014_53_5_a3/
%G ru
%F AL_2014_53_5_a3
D. O. Ptakhov. Primitive normality and additivity of free projective and strongly flat polygons. Algebra i logika, Tome 53 (2014) no. 5, pp. 614-624. http://geodesic.mathdoc.fr/item/AL_2014_53_5_a3/

[1] A. A. Stepanova, “Primitivno svyaznye i additivnye teorii poligonov”, Algebra i logika, 45:3 (2006), 300–313 | MR | Zbl

[2] A. A. Stepanova, “Poligony s primitivno normalnymi i additivnymi teoriyami”, Algebra i logika, 47:4 (2008), 491–508 | MR | Zbl

[3] V. Gould, A. V. Mikhalëv, E. A. Palyutin, A. A. Stepanova, “Teoretiko-modelnye svoistva svobodnykh, proektivnykh i ploskikh $S$-poligonov”, Fundament. prikl. matem., 14:7 (2008), 63–110 | MR

[4] B. Stenström, “Flatness and localization over monoids”, Math. Nachr., 48 (1971), 315–334 | DOI | MR | Zbl