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Homological Invariants of Local Rings

Published online by Cambridge University Press:  22 January 2016

Hiroshi Uehara
Hiroshi Uehara*
Affiliation:
State University of Iowa, Iowa-City, Iowa
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In this paper R is a commutative noetherian local ring with unit element 1 and M is its maximal ideal. Let K be the residue field R/M and let {t1,t2,…, tn) be a minimal system of generators for M. By a complex R<T1. . ., Tp> we mean an R-algebra* obtained by the adjunction of the variables T1. . ., Tp of degree 1 which kill t1,…, tp. The main purpose of this paper is, among other things, to construct an R-algebra resolution of the field K, so that we can investigate the relationship between the homology algebra H (R < T1,…, Tn>) and the homological invariants of R such as the algebra TorR(K, K) and the Betti numbers Bp = dimk TorR(K, K) of the local ring R. The relationship was initially studied by Serre [5].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 22 , June 1963 , pp. 219 - 227
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

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