AN INDEPENDENT RESULT FOR ATTACHED PRIMES OF CERTAIN TOR-MODULES
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Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let k ≥ 0 be an integer and r = Width>k(I,A) the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all t ≤ r the sets ( t∪ i=0 AttR(TorR i (R/In,A)))≥k and ( t∪ i=0 AttR(TorR i (R/(an1 1 , . . . , anl l ),A)))≥k are independent of the choice of n, n1, . . . , nl for any system of generators (a1, . . . , al) of I.
Abstract
Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let k ≥ 0 be an integer and r = Width>k(I,A) the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all t ≤ r the sets ( t∪ i=0 AttR(TorR i (R/In,A)))≥k and ( t∪ i=0 AttR(TorR i (R/(an1 1 , . . . , anl l ),A)))≥k are independent of the choice of n, n1, . . . , nl for any system of generators (a1, . . . , al) of I.
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