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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.
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참고문헌 (12)
참고문헌 신청
A. Ooishi / 1976 / Matlis duality and the width of a module / Hiroshima Math. J 6 (3) : 573 ~ 587
I. G. Macdonald / 1973 / Secondary representation of modules over a commutative ring / Sym-posia Mathematica(Convegno di Algebra Commutativa) 11 : 23 ~ 43
L. J. Ratliff / 1976 / On prime divisors of In, n large / Michigan Math. J 23 (4) : 337 ~ 352
L. Melkersson / 1993 / Asymptotic prime ideals related to derived functions / Proc. Amer. Math. Soc 117 (4) : 935 ~ 938
L. T. Nhan / 2012 / A Finiteness Result for Attached Primes of Certain Tor-Modules / Algebra Colloq 19 : 787 ~ 796
I. G. Macdonald / 1973 / Secondary representation of modules over a commutative ring / Sym-posia Mathematica(Convegno di Algebra Commutativa) 11 : 23 ~ 43
L. J. Ratliff / 1976 / On prime divisors of In, n large / Michigan Math. J 23 (4) : 337 ~ 352
L. Melkersson / 1993 / Asymptotic prime ideals related to derived functions / Proc. Amer. Math. Soc 117 (4) : 935 ~ 938
L. T. Nhan / 2012 / A Finiteness Result for Attached Primes of Certain Tor-Modules / Algebra Colloq 19 : 787 ~ 796
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