A Course In Commutative Algebra
by Robert B. Ash
Publisher: University of Illinois 2006
This is a text for a basic course in commutative algebra, it should be accessible to those who have studied algebra at the beginning graduate level. The book should help the student reach an advanced level as quickly and efficiently as possible.
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by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These lecture notes attempt to give a rapid review of the rudiments of classical commutative algebra. Topics covered: rings and modules, Noetherian rings, integral extensions, Dedekind domains, and primary decomposition of modules.
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The books cover birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, tilting theory, etc. These volumes reflect the lively interaction between the subjects.