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Valuations and semi-valuations of graded domains. (English) Zbl 0442.13002


MSC:

13A18 Valuations and their generalizations for commutative rings
16S34 Group rings
13G05 Integral domains
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References:

[1] Anderson, D.F.: Graded Krull domains. Comm. Algebra7, 79-106 (1979). · Zbl 0402.13013 · doi:10.1080/00927877908822334
[2] Anderson, D.F., Dobbs, D.: Pairs of rings with the same prime ideals. Canad. J. Math.32, 362-384 (1980) · Zbl 0479.13001 · doi:10.4153/CJM-1980-029-2
[3] Fuchs, L.: Infinite Abelian groups, Vol. I. New York: Academic Press 1970; Vol. II, 1973 · Zbl 0209.05503
[4] Gilmer, R., Parker, T.: Divisibility properties in semigroup rings. Michigan Math. J.21, 65-86 (1974) · Zbl 0285.13007 · doi:10.1307/mmj/1029001210
[5] Heinzer, W.:J-Noetherian integral domains with 1 in the stable range. Proc. Am. Math. Soc.19, 1369-1372 (1968) · Zbl 0167.31101
[6] Jaffard, P.: Les systèmes d’idéaux. Paris: Dunod 1960 · Zbl 0101.27502
[7] MacLane, S.: Homology. New York: Academic Press 1963
[8] Mott, J.L.: Nonsplitting sequences of value groups. Proc. Am. Math. Soc.44, 39-42 (1974) · Zbl 0286.13002 · doi:10.1090/S0002-9939-1974-0332770-X
[9] Northcott, D.: Lessons on rings, modules, and multiplicities. Cambridge: Cambridge University Press 1968 · Zbl 0159.33001
[10] Ohm, J.: Semi-valuations and groups of divisibility. Canad. J. Math.21, 576-591 (1969) · Zbl 0177.06501 · doi:10.4153/CJM-1969-065-9
[11] Passman, D.: The algebraic structure of group rings. New York: Wiley-Interscience 1977 · Zbl 0368.16003
[12] Schiffels, G.: Graduierte Ringe und Moduln. Bonn. Math. Schr.11, 1-122 (1960) · Zbl 0102.27603
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