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The grade of an ideal or module

  • D. Rees (a1)
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.

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COPYRIGHT: © Cambridge Philosophical Society 1957
References
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(1)Cartan, H.Extension du théorème des ‘chaines de syzygies’. R.C. Mat. R. Univ. Roma (5), 11 (1952), 156–66.
(2)Cohen, I.On the structure and ideal theory of complete local rings. Trans. Amer. Math. Soc. 59 (1946), 54–106.
(3)Grobner, W.Algebraische Geometrie (Vienna, 1949).
(4)Macaulay, F. S.The algebraic theory of modular systems (Cambridge, 1916).
(5)Northcott, D. G.On unmixed ideals in regular local rings. Proc. Lond. Math. Soc. (3) 3 (1953), 20–38.
(6)Rees, D.A theorem of homological algebra. Proc. Camb. Phil. Soc. 52 (1956), 605–10.
(7)Samuel, P.Sur la notion de multiplicitá en Algèbre et en Géométrie Algébrique. J. Math. pures appl. 30 (1951), 159–274.
(8)Samuel, P.Algèbre locale. Mem. Sci. Math. Fasc. 123 (1953).
(9)Serre, J.-P.Faisceaux Algébriques Cohérents. Ann. Math., Princeton, 61 (1955), 197–278.
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Mathematical Proceedings of the Cambridge Philosophical Society
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