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catalog contributor b12129720.
catalog created "c2001.".
catalog date "2001".
catalog date "c2001.".
catalog dateCopyrighted "c2001.".
catalog description "19. Integral Dependence and Finite Generation -- 20. Henselian Rings -- 21. Order and Rank in Local Rings. Regular Local Rings -- 22. Another Proof that a Formal Power Series Rings in Noetherian -- Ch. IV. Parameters in Power Series Rings -- 23. Parameters for Ideals -- 24. Perfect Fields -- 25. Regularity of Quotient Rings -- 26. Translates of Ideals -- 27. Dimension of an Intersection -- 28. Algebraic Lemmas on Algebroid Functions -- Ch. V. Analytic Sets -- 29. The Language of Germs -- 30. Decomposition of an Analytic Set Germ -- 31. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ -- 32. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary) -- 33. Local Properties of Analytic Sets -- 34. Connectivity Properties of Complex Analytic Sets -- 35. Parametrization of a Pure Dimensional Analytic Set -- 36. Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties -- ".
catalog description "37. Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow -- 38. Topological Dimension -- 39. Remarks on the Fundamental Group -- Ch. VI. Language of Sheaves -- 40. Inductive Systems and Presheaves -- 41. Sheaves -- 42. Coherent Sheaves -- Ch. VII. Analytic Spaces -- 43. Definitions -- 44. Recapitulation of Properties of Analytic Spaces -- 45. Invariance of Order and Rank -- 46. Bimeromorphic Maps and Normalizations.".
catalog description "Ch. 1. Elementary Theory in C[superscript n] -- 1. Notation and Terminology -- 2. Convergent Power Series -- 3. Laurent Series -- 4. Cauchy Theory -- 5. Convexity in R[superscript n] -- 6. Laurent Expansion in C[superscript n] -- 7. Domains of Holomorphy -- 8. A Theorem of Rado -- 9. Comments on Totally Disconnected Fields -- Ch. II. Weierstrass Preparation Theorem -- 10. Weierstrass Preparation Theorem. Identity Theorem, Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem -- 11. Continuity of Roots and Open Map Theorem -- 12. Hensel's Lemma. Continuity of Algebroid Functions -- 13. Complex Weierstrass Preparation Theorem -- 14. Riemann Extension Theorem and Connectivity of Algebroid Hypersurface -- 15. Oka Coherence -- 16. Cartan Module Bases -- Ch. III. Review from Local Algebra -- 17. Depth, Height, and Dimension, Completions. Direct Sums Resultants and Discriminants -- 18. Quotient Rings -- ".
catalog description "Includes bibliographical references (p. 471-474) and indexes.".
catalog extent "xv, 488 p. :".
catalog identifier "981024505X".
catalog issued "2001".
catalog issued "c2001.".
catalog language "eng".
catalog publisher "Singapore ; River Edge, NJ : World Scientific,".
catalog subject "Geometry, Analytic.".
catalog subject "QA551 .A24 2001".
catalog tableOfContents "19. Integral Dependence and Finite Generation -- 20. Henselian Rings -- 21. Order and Rank in Local Rings. Regular Local Rings -- 22. Another Proof that a Formal Power Series Rings in Noetherian -- Ch. IV. Parameters in Power Series Rings -- 23. Parameters for Ideals -- 24. Perfect Fields -- 25. Regularity of Quotient Rings -- 26. Translates of Ideals -- 27. Dimension of an Intersection -- 28. Algebraic Lemmas on Algebroid Functions -- Ch. V. Analytic Sets -- 29. The Language of Germs -- 30. Decomposition of an Analytic Set Germ -- 31. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ -- 32. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary) -- 33. Local Properties of Analytic Sets -- 34. Connectivity Properties of Complex Analytic Sets -- 35. Parametrization of a Pure Dimensional Analytic Set -- 36. Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties -- ".
catalog tableOfContents "37. Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow -- 38. Topological Dimension -- 39. Remarks on the Fundamental Group -- Ch. VI. Language of Sheaves -- 40. Inductive Systems and Presheaves -- 41. Sheaves -- 42. Coherent Sheaves -- Ch. VII. Analytic Spaces -- 43. Definitions -- 44. Recapitulation of Properties of Analytic Spaces -- 45. Invariance of Order and Rank -- 46. Bimeromorphic Maps and Normalizations.".
catalog tableOfContents "Ch. 1. Elementary Theory in C[superscript n] -- 1. Notation and Terminology -- 2. Convergent Power Series -- 3. Laurent Series -- 4. Cauchy Theory -- 5. Convexity in R[superscript n] -- 6. Laurent Expansion in C[superscript n] -- 7. Domains of Holomorphy -- 8. A Theorem of Rado -- 9. Comments on Totally Disconnected Fields -- Ch. II. Weierstrass Preparation Theorem -- 10. Weierstrass Preparation Theorem. Identity Theorem, Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem -- 11. Continuity of Roots and Open Map Theorem -- 12. Hensel's Lemma. Continuity of Algebroid Functions -- 13. Complex Weierstrass Preparation Theorem -- 14. Riemann Extension Theorem and Connectivity of Algebroid Hypersurface -- 15. Oka Coherence -- 16. Cartan Module Bases -- Ch. III. Review from Local Algebra -- 17. Depth, Height, and Dimension, Completions. Direct Sums Resultants and Discriminants -- 18. Quotient Rings -- ".
catalog title "Local analytic geometry / Shreeram Shankar Abhyankar.".
catalog type "text".