Smoothness, regularity and complete intersection
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.
Read More ↓Title Statements
- Full title :Smoothness, regularity and complete intersection / Javier Majadas, Antonio G. Rodicio.
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.
Read More ↓Edition Statements
- Publication Date:2010.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2010.
The Physical Object
- Description:1 online resource (vi, 134 p. :) : il.
Edition Identifiers
- ISBN:9780521125727, 0521125723, 9781139127820, 1139127829, 9781139114998, 1139114999, 9781139107181, 1139107186, 9781139117166, 1139117165
- oclc:on1105543078
- Dewey Decimal:512.44
Table of 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 smoo…
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