Linear Forms on Modules of Projective Dimension One
نویسنده
چکیده
Proposition 1. Assume that r = n − m > 1 and that the first nonvanishing Fitting ideal of M has grade r + 1. Then the following conditions are equivalent. (1) There is a χ ∈ M∗ = HomR(M,R) such that the ideal Imχ has grade r + 1. (2) There exists a submodule U of M with the following properties: (i) rankU = r − 1; (ii) U is reflexive, orientable, and Up is a free direct summand of Mp for all primes p of R such that grade p ≤ r. (3) m = 1 and r is odd.
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تاریخ انتشار 2004