Smoke, William Dimension and multiplicity for graded algebras. (English) Zbl 0231.13006 J. Algebra 21, 149-173 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 15 Documents 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 PDFBibTeX XMLCite \textit{W. Smoke}, J. Algebra 21, 149--173 (1972; Zbl 0231.13006) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.