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Smoothness, regularity and complete intersection.


Smoothness, regularity and complete intersection.

Majadas, Javier and Antonio G. Rodicio.

Cambridge U. Press


133 pages



London Mathematical Society lecture note series; 373


There are important theorems that are commonly treated in advanced books on commutative algebra without proofs, because the existing proofs are so difficult, say Majadas and Rodicio (both U. de Santiago de Compostela, Spain). They provide homological proofs for a number of them, modifying the original proofs that involve simplicial methods, so they use only lower dimensional homology modules that they can introduce in an ad hoc manner, thus avoiding simplicial theory altogether. They cover the definition and first properties of homology and co-homology modules, formally smooth homomorphisms, the structure of complete noetherian local rings, complete intersections, Popescu's theorem of regular homomorphisms, and the localization of formal smoothness.

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Publication:SciTech Book News
Article Type:Book review
Date:Sep 1, 2010
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