Vol. 109, No. 1, 1983

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The determinantal ideals of link modules. II

Lorenzo Traldi

Vol. 109 (1983), No. 1, 237–245
Abstract

Let H be the multiplicative free abelian group of rank m 1. Suppose 0 B A IH 0 is a short exact sequence of ZH-modules, and the module A is finitely generated. Then B is also a finitely generated ZH-module, and for any k Z the determinantal ideals of A and B satisfy the equality

Ek (A) : (IH )p = Ek−1(B) : (IH)q

for all sufficiently large values of p and q. Furthermore, if this exact sequence is the link module sequence of a tame link of m components in S3, then

                      m−1
Ek(A) = Ek−1(B) : (IH )( 2 )

whenever k m.

Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 13A15, 13E15
Milestones
Received: 27 January 1982
Published: 1 November 1983
Authors
Lorenzo Traldi