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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Kaplansky, I. (2010). The Theory of Homological Dimension. In: Herstein, I.N. (eds) Some Aspects of Ring Theory. C.I.M.E. Summer Schools, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11036-8_4
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