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Le théorème des zéros en géométries algébrique et analytique réelles. (French) Zbl 0328.14001

MSC:
14A05Relevant commutative algebra
26E05Real-analytic functions
32C05Real-analytic manifolds and spaces
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Full Text: Numdam EuDML
References:
[1] ARTIN M .- On the solutions of analytic equations , Invent. Math., Berlin, t. 5, 1968 , p. 277-291. MR 38 #344 | Zbl 0172.05301 · Zbl 0172.05301 · doi:10.1007/BF01389777 · eudml:141922
[2] BOCHNAK J .- Sur le théorème des zéros de Hilbert ”différentiable” , Topology, London, t. 12, 1973 , p. 417-424. MR 48 #12590 | Zbl 0282.58003 · Zbl 0282.58003 · doi:10.1016/0040-9383(73)90033-5
[3] BOCHNAK (J.) et RISLER (J.-J.) .- Le théorème des zéros pour les variétés analytiques de dimension 2 , Ann. Éc. Norm. Sup., t. 8, 1975 , p. 353-364. Numdam | MR 53 #854 | Zbl 0315.14008 · Zbl 0315.14008 · numdam:ASENS_1975_4_8_3_353_0 · eudml:81961
[4] DUBOIS (D. W.) .- A nullstellensatz for ordered fielsd , Arkiv for Mat., Stockholm, t. 8, 1969 , p. 111-114. MR 42 #7642 | Zbl 0205.06102 · Zbl 0205.06102 · doi:10.1007/BF02589551
[5] EFROYMSON (G.) .- Local reality on algebraic varieties , J. of Algebra, t. 29, 1974 , p. 133-142. MR 51 #495 | Zbl 0275.14018 · Zbl 0275.14018 · doi:10.1016/0021-8693(74)90118-5
[6] GALBIATI (M.) et TOGNOLI (A.) .- Alcune proprieta delle varieta algebriche reali , Ann. Sc. N. Sup. Pisa, série 3, t. 27, 1973 , p. 359-404. Numdam | MR 51 #493 | Zbl 0277.14010 · Zbl 0277.14010 · numdam:ASNSP_1973_3_27_3_359_0 · eudml:83639
[7] HIRONAKA (H.) .- Introduction to real-analytic sets and real-analytic maps , Cours à l’Istituto Matematico L. Tonelli dell’Universitá da Pisa, 1973 . MR 57 #16665
[8] JACOBSON (N.) .- Lectures in abstract algebra , vol. 3.- Princeton, D. Van Nostrand Company, 1964 (University Series in higher Mathematics). Zbl 0124.27002 · Zbl 0124.27002
[9] LASSALLE (G.) .- Le théorème des zéros formels , Université d’Orsay (preprint).
[10] MALGRANGE (B.) .- Ideals for differentiable functions .- Bombay, Oxford Unisity Press, 1966 (Tata Institute for fundamental Research. Studies in Mathematics, 3). Zbl 0177.17902 · Zbl 0177.17902
[11] MERRIEN (J.) .- Idéaux de l’anneau des séries formelles à coefficients réels et variétés associées , J. Math. pures et appl., t. 51, 1972 , p. 169-187. MR 47 #7768 | Zbl 0241.13009 · Zbl 0241.13009
[12] MERRIEN (J.) .- Un théorème des zéros pour les idéaux de séries formelles à coefficients réels , C.R. Acad. Sc. Paris, t. 276, 1973 , série A, p. 1055-1058. MR 47 #4976 | Zbl 0252.14001 · Zbl 0252.14001
[13] MOSTOWSKI (T.) .- On the ring of global Nash functions , Warzawa, 1974 (preprint).
[14] NARASIMHAN (R.) .- Introduction to the theory of analytic spaces .- Berlin, Springer-Verlag, 1966 (Lecture Notes in Mathematics, 25). MR 36 #428 | Zbl 0168.06003 · Zbl 0168.06003 · doi:10.1007/BFb0077071
[15] RISLER (J.-J.) .- Une caractérisation des idéaux des variétés algébriques réelles , C. R. Acad. Sc. Paris, t. 271, 1970 , série A, p. 1171-1173. MR 43 #202 | Zbl 0211.53401 · Zbl 0211.53401
[16] RISLER (J.-J.) .- Un théorème des zéros en géométrie analytique réelle , C. R. Acad. Sc. Paris, t. 274, 1972 , série A, p. 1488-1490. MR 45 #3754 | Zbl 0236.14001 · Zbl 0236.14001
[17] RISLER (J.-J.) .- Un théorème des zéros pour les idéaux de fonctions différentiables , Ann. Inst. Fourier, Grenoble, t. 26, 1976 , fasc. 3. Numdam | MR 54 #13108 | Zbl 0324.46028 · Zbl 0324.46028 · doi:10.5802/aif.626 · numdam:AIF_1976__26_3_73_0 · eudml:74295
[18] ROBINSON (A.) .- Further remarks on ordered fielsd on definite functions , Math. Annalen, t. 130, 1956 , p. 405-409. MR 17,1180e | Zbl 0071.26401 · Zbl 0071.26401 · doi:10.1007/BF01343235 · eudml:160472
[19] SERRE (J.-P.) .- Faisceaux algébriques cohérents , Annals of Math., t. 61, 1955 , p. 197-278. MR 16,953c | Zbl 0067.16201 · Zbl 0067.16201 · doi:10.2307/1969915