Linear complementary inequalities for orders of germs of analytic functions. (English) Zbl 0497.32005


32B10 Germs of analytic sets, local parametrization
32B20 Semi-analytic sets, subanalytic sets, and generalizations
32Q99 Complex manifolds
14B05 Singularities in algebraic geometry
Full Text: DOI EuDML


[1] [B] Becker, J.: Exposé on a conjecture of Tougeron. Ann. Inst. Fourier (Grenoble)27, 4, 9-27 (1977) · Zbl 0337.14002
[2] [B-Z] Becker, J., Zame, W.R.: Applications of functional analysis to the solution of power series equations. Math. Ann.243, 37-54 (1979) · Zbl 0413.13015
[3] [B-R] Bloom, T., Risler, J.-J.: Familles de courbes sur les germes d’espaces analytiques. Bull. Soc. Math. France105, 261-280 (1977) · Zbl 0365.32003
[4] [Bo-R] Bochnack, J., Risler, J.-J.: Sur les exposants de ?ojasiewicz. Comment. Helv.50, 493-507 (1975) · Zbl 0321.32006
[5] [F] Fischer, G.: Complex analytic geometry (LNM 538). Berlin-Heidelberg-New York: Springer 1976
[6] [G] Gabrièlov, A.M.: Formal relations between analytic functions. Izv. Akad. Nauk. SSSR.37, 1056-1088 (1973)
[7] [G-R] Grauert, H., Remmert, R.: Analytische Stellenalgebren (GMW 176). Berlin-Heidelberg-New York: Springer 1971
[8] [H1] Hironaka, H.: Subanalytic sets. In: Number theory, algebraic geometry and commutative algebra, in honor of Y. Akizuki, pp. 453-493. Tokyo: Kinonuniya 1973
[9] [H2] Hironaka, H.: Introduction to real-analytic sets and real-analytic maps. Istituto matematico ?L. Tonelli? dell Universita di Pisa 1973
[10] [H-W] Hurewicz, W., Wallman H.: Dimension theory. Princeton Univ. Press 1948
[11] [I] Izumi, S.: Remarks on order of a function on an analytic space. In: Singularities of differentiable mappings (RIMS Kokyuroku 403), pp. 104-107. Res. Inst. for Math. Sci., Kyoto Univ. 1980
[12] [L-T] Lejeune-Jalabert, M., Teissier B.: Clôture intégrale des idéaux et équisingularite (chapitre 1). École Polytechnique 1974
[13] [M] Matsumara, H.: Commutative algebra, 2nd edition (MLNS56). Massachusetts: Benjamin/Cummings 1980
[14] [Mi] Milman, P.D.: Analytic and polynomial homomorphisms of analytic rings. Math. Ann.232, 247-253 (1978) · Zbl 0363.32007
[15] [R1] Risler, J.-J.: Les exposants de ?ojasiewicz dans le cas analytique réel. (appendix of [L-T])
[16] [R2] Risler, J.-J.: Sur la divisibilité des fonctions de classeC? par les fonctions analytiques réelles. Bull. Soc. Math. France105, 97-112 (1977)
[17] [S] Spallek, K.:l-Platte Funktionen auf semianalytischen Mengen. Math. Ann.227, 277-286 (1977) · Zbl 0346.32038
[18] [T1] Tougeron, J.-Cl.: Idéaux de fonctions différentiables (EMIG 71). Berlin-Heidelberg-New York: Springer 1972
[19] [T2] Tougeron, J.-Cl.: Courbes analytiques sur un germ d’espace analytique et applications. Ann. Inst. Fourier (Grenoble)26, (2) 117-131 (1976) · Zbl 0318.32005
[20] [T3] Tougeron, J.-Cl.: Fonctions composées différentiables: Cas algébrique. Ann. Inst. Fourier (Grenoble)30, 4, 51-74 (1980)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.