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Multiplicities in graded rings II: integral equivalence and the Buchsbaum–Rim multiplicity

Published online by Cambridge University Press:  24 October 2008

D. Kirby  and
D. Rees
D. Kirby
Affiliation:
The University, Southampton SO9 5NH
D. Rees
Affiliation:
6 Hillcrest Park, Exeter EX4 4SH, Devon
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Extract

While this paper is principally a continuation of [5], with as its object the application of sections 6 and 7 of that paper to obtain results related to the Buchsbaum–Rim multiplicity, it also has connections with [8] which are the subject of the first of the four sections. These concern integral equivalence of finitely generated R-modules. where R is an arbitrary noetherian ring. We therefore introduce a finitely generated R-module M and relate to it a short exact sequence (s.e.s.),

where F is a free module generated by m elements u1,…, um, and L is generated by elements yj, (j = 1, …, n), of F. We identify the elements u1, …, um with a set of indeterminates X1, …, Xm, and F with the R-module S1 of elements of degree 1 of the graded ring S = R[X1, …, Xm].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 3 , April 1996 , pp. 425 - 445
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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