Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2014_26_5_a4, author = {B. Ya. Kazarnovskiǐ and A. G. Hovanskiǐ}, title = {The tropical {Noetherity} and {Gr\"obner} bases}, journal = {Algebra i analiz}, pages = {142--163}, publisher = {mathdoc}, volume = {26}, number = {5}, year = {2014}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2014_26_5_a4/} }
B. Ya. Kazarnovskiǐ; A. G. Hovanskiǐ. The tropical Noetherity and Gr\"obner bases. Algebra i analiz, Tome 26 (2014) no. 5, pp. 142-163. http://geodesic.mathdoc.fr/item/AA_2014_26_5_a4/
[1] De Concini C., Procesi C., “Complete symmetric varieties. II”, Intersection theory Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983), Adv. Stud. Pure Math., 6, North-Holland, Amsterdam, 1985, 481–513 | MR
[2] De Concini C., “Equivariant embeddings of homogeneous spaces”, Proc. Intern. Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, 2, Amer. Math. Soc., Providence, RI, 1987, 369–377 | MR
[3] Fulton W., Sturmfels B., “Intersection theory on toric varieties”, Topology, 36:2 (1997), 335–353 | DOI | MR | Zbl
[4] Kazarnovskii B. Ya., “Ukorocheniya sistem uravnenii, idealov i mnogoobrazii”, Izv. RAN. Ser. mat., 63:3 (1999), 119–132 | DOI | MR | Zbl
[5] Seidenberg A., “On the length of a Hilbert ascending chain”, Proc. Amer. Math. Soc., 29 (1971), 443–450 | DOI | MR | Zbl
[6] Seidenberg A., “Constructive proof of Hilbert's theorem on ascending chains”, Trans. Amer. Math. Soc., 174 (1972), 305–312 | MR
[7] Moreno-Socias G., “Length of polynomial ascending chains and primitive recursiveness”, Math. Scand., 71:2 (1992), 181–205 | MR | Zbl
[8] Kazarnovskii B. Ya., “$c$-veery i mnogogranniki Nyutona algebraicheskikh mnogoobrazii”, Izv. RAN. Ser. mat., 67:3 (2003), 23–44 | DOI | MR | Zbl
[9] Mikhalkin G., “Counting curves via lattice paths in polygons”, C. R. Math. Acad. Sci. Paris, 336:8 (2003), 629–634 | DOI | MR | Zbl
[10] Shustin E., “A tropical approach to enumerative geometry”, Algebra i analiz, 17:2 (2005), 170–214 | MR | Zbl
[11] Itenberg I., Mikhalkin G., Shustin E., Tropical algebraic geometry, 2nd ed., Birkhauser, Basel, 2009 | MR | Zbl
[12] Kazarnovskii B., Khovanskii A., Algebra i tropicheskaya geometriya, 2011–2013, 42 pp., (gotovitsya k publikatsii)
[13] Chulkov S., Khovanskii A., Geometriya polugruppy $\mathbb Z^n_{\geq0}$. Prilozheniya k algebre, kombinatorike i differentsialnym uravneniyam, MTsNMO, M., 2006
[14] Mora F., Robbiano L., “The Gröbner fan of an ideal. Computational aspects of commutative algebra”, J. Symbolic Comput., 6:2–3 (1988), 183–208 | DOI | MR | Zbl
[15] Weispfenning V., “Constructing universal Gröbner bases”, Lecture Notes in Comput. Sci., 356, Springer, Berlin, 1989, 408–417 | DOI | MR
[16] Schwartz N., “Stability of Gröbner bases”, J. Pure Appl. Algebra, 53:1–2 (1988), 171–186 | DOI | MR | Zbl
[17] Kazarnovskii B., Khovanskii A., “Universalnyi bazis Grëbnera”, Proc. Intern. Conf. on Polynomial Computer Algebra, St. Peterburg, 2011, 65–69
[18] Macaulay F. S., The algebraic theory of modular systems, Cambridge Tracts in Math. and Math. Phys., 19, Cambridge Univ. Press, Cambridge, 1916 | MR
[19] Sauer Th., “Gröbner bases, $H$-bases and interpolations”, Trans. Amer. Math. Soc., 353:6 (2001), 2293–2308, (electronic) | DOI | MR | Zbl