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Dimension and multiplicity for graded algebras. (English) Zbl 0231.13006


MSC:

13A02 Graded rings
13D15 Grothendieck groups, \(K\)-theory and commutative rings
13D05 Homological dimension and commutative rings
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13E15 Commutative rings and modules of finite generation or presentation; number of generators
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References:

[1] Bourbaki, N., Éléments, Algèbre Commutative (1961), Hermann: Hermann Paris, Chap. 4 · Zbl 0108.04002
[2] Eilenberg, S., Homological dimension and syzygies, Ann. of Math., 64, 328-336 (1956) · Zbl 0073.26003
[3] Fraser, M., Multiplicities and Grothendieck groups, Trans. Amer. Math. Soc., 136, 77-92 (1969) · Zbl 0172.05103
[4] Hilbert, D., Ueber die Theorie der algebraischen Formen, Math. Ann., 36, 473-534 (1890) · JFM 22.0133.01
[5] Koszul, J. L., Sur un type d’algèbres différentielles en rapport avec la transgression, (Colloque de Topologie (1950)), 73-81, Brussels · Zbl 0045.30801
[6] Serre, J. P., Algèbre Locale-Multiplicités (1965), Springer-Verlag: Springer-Verlag New York · Zbl 0091.03701
[7] Smoke, W., Dimension and multiplicity for graded algebras (Research announcement), Bull. Amer. Math. Soc., 76, 743-746 (1970) · Zbl 0194.34801
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