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 wellknown important results found in standard books on commutative algebra. It also serves as a friendly introduction to the powerful methods used in the AndreQuillen homology of commutative algebras 
Bibliography 
Includes bibliographical references (pages 130133) and index 
Notes 
Print version record 
Subject 
Commutative algebra.

Form 
Electronic book

Author 
Rodicio, Antonio G.

ISBN 
0521125723 (paperback) 

1139107186 (electronic bk.) 

1139114999 

1139117165 

1139127829 (electronic bk.) 

9780521125727 (paperback) 

9781139107181 (electronic bk.) 

9781139114998 

9781139117166 

9781139127820 (electronic bk.) 
