The Theory of Homological Dimension

2011
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Author: Irving Kaplansky
Published in: Some Aspects of Ring Theory
Publisher: Springer Berlin Heidelberg

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Abstract

In their basic treatise [4], Cartan and Eilenberg treat homological dimension as a peripheral aspect of the general theory being developed, and so do the later books by Northcott [13] and Mac Lane[9]. In the meantime a more or less self-contained theory of homological dimension has come into being. A good account of the portions relevant for local rings appears in the book of Nagata [l2].In these lectures I will “revisit” the account given in my mimeographed notes of 1959 [5], and I will add further relevant material on R-sequences and unique factorization. Where there is some novelty, proofs will be sketched.

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previous chapter Representation Theory of Jordan Algebras

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Metadata

Title: The Theory of Homological Dimension
Author: Irving Kaplansky
Publisher: Springer Berlin Heidelberg
Book: Some Aspects of Ring Theory
Print ISBN: 978-3-642-11035-1

Electronic ISBN: 978-3-642-11036-8

Copyright Year: 2011
DOI: https://doi.org/10.1007/978-3-642-11036-8_4