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Author Majadas, Javier.

Title Smoothness, regularity and complete intersection / Javier Majadas, Antonio G. Rodicio
Published Cambridge ; New York : Cambridge University Press, 2010
Online access available from:
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Description 1 online resource (vi, 134 pages) : illustrations
Series London Mathematical Society lecture note series ; 373
London Mathematical Society lecture note series ; 373
Contents Cover; Title; Copyright; Contents; Introduction; 1 Definition and first properties of (co- )homology modules; 1.1 First definition; 1.2 Differential graded algebras; 1.3 Second definition; 1.4 Main properties; 2 Formally smooth homomorphisms; 2.1 Infinitesimal extensions; 2.2 Formally smooth algebras; 2.3 Jacobian criteria; 2.4 Field extensions; 2.5 Geometric regularity; 2.6 Formally smooth local homomorphisms of noetherian rings; 2.7 Appendix: The Mac Lane separability criterion; 3 Structure of complete noetherian local rings; 3.1 Cohen rings; 3.2 Cohen's structure theorems
4 Complete intersections4.1 Minimal DG resolutions; 4.2 The main lemma; 4.3 Complete intersections; 4.4 Appendix: Kunz's theorem on regular local rings in characteristic p; 5 Regular homomorphisms: Popescu's theorem; 5.1 The Jacobian ideal; 5.2 The main lemmas; 5.3 Statement of the theorem; 5.4 The separable case; 5.5 Positive characteristic; 5.6 The module of differentials of a regular homomorphism; 6 Localization of formal smoothness; 6.1 Preliminary reductions; 6.2 Some results on vanishing of homology; 6.3 Noetherian property of the relative Frobenius
6.4 End of the proof of localization of formal smoothness6.5 Appendix: Power series; Appendix: Some exact sequences; Bibliography; Index
Summary This short book gives complete and relatively easy proofs of well-known important results found in standard books on commutative algebra. It also serves as a friendly introduction to the powerful methods used in the Andre-Quillen homology of commutative algebras
Bibliography Includes bibliographical references (pages 130-133) and index
Notes Print version record
Subject Commutative algebra.
Form Electronic book
Author Rodicio, Antonio G.
ISBN 0521125723 (paperback)
1139107186 (electronic bk.)
1139127829 (electronic bk.)
9780521125727 (paperback)
9781139107181 (electronic bk.)
9781139127820 (electronic bk.)