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The grade of an ideal or module

Published online by Cambridge University Press:  24 October 2008

D. Rees
D. Rees
Affiliation:
Downing CollegeCambridge
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Extract

In (6), the author introduced a numerical character of an ideal of a Noether ring A, called the grade of . This can be defined as the least integer k such that (the definition given in (6) differed from this, but, as will be seen below, is equivalent). The purpose of the present paper is to study this character in more detail.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 28 - 42
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Cartan, H.Extension du théorème des ‘chaines de syzygies’. R.C. Mat. R. Univ. Roma (5), 11 (1952), 156–66.Google Scholar
(2)Cohen, I.On the structure and ideal theory of complete local rings. Trans. Amer. Math. Soc. 59 (1946), 54–106.CrossRefGoogle Scholar
(3)Grobner, W.Algebraische Geometrie (Vienna, 1949).CrossRefGoogle Scholar
(4)Macaulay, F. S.The algebraic theory of modular systems (Cambridge, 1916).CrossRefGoogle Scholar
(5)Northcott, D. G.On unmixed ideals in regular local rings. Proc. Lond. Math. Soc. (3) 3 (1953), 20–38.CrossRefGoogle Scholar
(6)Rees, D.A theorem of homological algebra. Proc. Camb. Phil. Soc. 52 (1956), 605–10.CrossRefGoogle Scholar
(7)Samuel, P.Sur la notion de multiplicitá en Algèbre et en Géométrie Algébrique. J. Math. pures appl. 30 (1951), 159–274.Google Scholar
(8)Samuel, P.Algèbre locale. Mem. Sci. Math. Fasc. 123 (1953).Google Scholar
(9)Serre, J.-P.Faisceaux Algébriques Cohérents. Ann. Math., Princeton, 61 (1955), 197–278.CrossRefGoogle Scholar