Tropical polynomial algebras
- [1] Laboratoire d’Informatique et de Mathématiques Université de la Réunion Pôle Technologique Universitaire Bâtiment 2, 2 rue Joseph Wetzell 97490 Sainte Clotilde, France
Annales mathématiques Blaise Pascal (2013)
- Volume: 20, Issue: 2, page 301-330
- ISSN: 1259-1734
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top- M. Akian, R. Bapat, S. Gaubert, Max-plus algebras, Chapter 25 in the Handbook of Linear Algebra,, Discrete Mathematics and Its Applications, Volume 39, (2007), Chapman and Hall
- F. Aroca, Krull-tropical hypersurfaces, Annales de la faculté des sciences de Toulouse (2010), 525-538 Zbl1223.14069MR2790807
- S. Banerjee, Tropical geometry over higher dimensional local fields, arXiv : 1105.5873 v2 (2012) Zbl06387020
- D. Castella, L’algèbre tropicale comme algèbre de la caractéristique 1 : Polynômes rationnels et fonctions polynomiales, arXiv : 0809.0231 (2008)
- D. Castella, Eléments d’algèbre linéaire tropicale, Linear Algebra and Its Applications 432 (2010), 1460-1474 Zbl1234.15009MR2580441
- D. Grigoriev, On a tropical dual Nullstellensatz, Adv. Appl. Math. 48 (2012), 457-464 Zbl1247.14067MR2873889
- U. Hebisch, H.J. Weinert, Semirings. Algebraic theory and application in computer sciences, (1998), World scientific, Singapore Zbl0934.16046MR1704233
- Ilia Itenberg, Grigory Mikhalkin, Eugenii Shustin, Tropical algebraic geometry, 35 (2009), Birkhäuser Verlag, Basel Zbl1165.14002MR2508011
- Z. Izhakian, Tropical algebraic sets ideals and an algebraic Nullstellensatz, IJAC 18(6) (2008), 1067-1098 Zbl1231.14054MR2447149
- Z. Izhakian, L. Rowen, The tropical rank of a tropical matrix, Comm. in Algebra 37 (2009), 3912-3927 Zbl1184.15003MR2573227
- Z. Izhakian, L. Rowen, Supertropical algebra, Adv. in Math. 225 (2010), 2222-2286 Zbl1273.14132MR2680203
- V. N. Kolokoltsov, V. P. Maslov, Idempotent analysis and its applications, (1997), Kluver academic publishers, Dordrecht Zbl0941.93001MR1447629
- P. Lescot, Absolute algebra II Ideals and spectra, J. of Pure and Applied Algebra 215(7) (2011), 1782-1790 Zbl1243.06013MR2771645
- G. L. Litvinov, V. P. Maslov, Idempotent Mathematics and Mathematical Physics, Number 377 (2005), Contemp. Math. Amer. Math. Soc. Zbl1069.00011MR2145152
- G. Mikhalkin, Amoebas of algebraic varieties and tropical geometry, Different faces of geometry (2004), 257-300, Int. Math. Ser.(N.Y.)vol.3v. Zbl1072.14013MR2102998
- G. Mikhalkin, Decomposition into pairs-of-plants for complex algebraic hypersurfaces, Topology 43(5) (2004), 1035-1065 Zbl1065.14056MR2079993
- J. Richter-Gebert, B. Sturmfels, T. Theobland, First steps in tropical geometry, Contemporary Mathematics 377 (2005), 289-317 Zbl1093.14080MR2149011
- E. Shustin, Z. Izhakian, A tropical Nullstellensatz, Proc. Amer. Math. Soc. 135 (12) (2007), 3815-3821 Zbl1163.12004MR2341931
- D.E. Speyer, B. Sturmfels, Tropical mathematics, Mathematics Magazine 82 (3) (2009), 163-173 Zbl1227.14051MR2522909
- L. Tabera, Tropical resultants for curves and stable intersection, Rev. Mat. Iberoam 24 (2008), 941-961 Zbl1216.14048MR2490204
- O. Viro, Dequantization of real algebraic geometry on logarithm, European Congress of Mathematics, Vol. I, Barcelone (2001), 135-146, 201Progress Math.P. M. Zbl1024.14026