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Hilbert functions and the extension functor

Published online by Cambridge University Press:  04 October 2011

David Kirby
David Kirby
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton S09 5NH
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Throughout R will denote a commutative ring with identity, A,B etc. will denote ideals of R, and E will denote a unitary R-module. We recall from [5] the definition of homological grade hgrR(A;E) as inf{r|ExtRr(R/A,E) ≠ 0}, and we allow both hgrR(A;E) = ∞ (i.e. ExtRr(R/A,E) = 0 for all r) and AE = E. For the most part E will be Noetherian, in which case hgrR(A;E) coincides with the usual grade grR(A;E) which is the supremum of the lengths of the (weak) E-sequences contained in A (see [7], for example).

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 441 - 446
Copyright
Copyright © Cambridge Philosophical Society 1989

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