Geodesic
Axiomatizability of free $S$-posets
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 99-115.

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

In this work, we investigate the partially ordered monoids $S$ over which the class of free (over a poset) $S$-posets is axiomatizable. Similar questions for $S$-sets were considered in papers of V. Gould, S. Bulman-Fleming, and A. A. Stepanova. 
@article{FPM_2009_15_1_a6,
     author = {M. A. Pervukhin and A. A. Stepanova},
     title = {Axiomatizability of free $S$-posets},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {99--115},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a6/}
}
TY  - JOUR
AU  - M. A. Pervukhin
AU  - A. A. Stepanova
TI  - Axiomatizability of free $S$-posets
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2009
SP  - 99
EP  - 115
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a6/
LA  - ru
ID  - FPM_2009_15_1_a6
ER  - 
%0 Journal Article
%A M. A. Pervukhin
%A A. A. Stepanova
%T Axiomatizability of free $S$-posets
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2009
%P 99-115
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a6/
%G ru
%F FPM_2009_15_1_a6
M. A. Pervukhin; A. A. Stepanova. Axiomatizability of free $S$-posets. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 99-115. http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a6/

[1] Gabriel P., Tsisman M., Kategorii chastnykh i teoriya gomologii, Mir, M., 1971 | Zbl

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

[3] Keisler G., Chen Ch., Teoriya modelei, Mir, M., 1977 | MR

[4] Klifford A., Preston G., Algebraicheskaya teoriya polugrupp, Mir, M., 1971

[5] Pervukhin M. A., Stepanova A. A., “Aksiomatiziruemost i polnota nekotorykh klassov chastichno uporyadochennykh poligonov”, Algebra i logika, 48:1 (2009), 90–121 | MR | Zbl

[6] Stepanova A. A., “Aksiomatiziruemost i polnota nekotorykh klassov $S$-poligonov”, Algebra i logika, 3:5 (1991), 583–594 | MR

[7] Bulman-Fleming S., Gould V., “Axiomatisability of weakly flat, flat and projective $S$-sets”, Commun. Algebra, 30 (2002), 5575–5593 | DOI | MR | Zbl

[8] Fountain J. B., “Perfect semigroups”, Proc. Edinburgh Math. Soc., 20 (1976), 87–93 | DOI | MR | Zbl

[9] Gould V., “Axiomatisability problems for $S$-systems”, J. London Math. Soc., 35:2 (1987), 193–201 | DOI | MR | Zbl

[10] Kilp M., Knauer U., Mikhalev A. V., Monoids, Acts and Categories, Walter de Gruyter, Berlin, 2000 | MR | Zbl

[11] Knauer U., “Projectivity of acts and Morita equivalence of monoids”, Semigroup Forum, 3 (1972), 359–370 | DOI | MR | Zbl

[12] Shi X., “Strongly flat and po-flat $S$-posets”, Commun. Algebra, 33 (2005), 4515–4531 | DOI | MR | Zbl

[13] Shi X., Liu Z., Wang F., Bulman-Fleming S., “Indecomposable, projective and flat $S$-posets”, Commun. Algebra, 33 (2005), 235–251 | DOI | MR | Zbl

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