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Unmixed 2-dimensional local domains
Stephen Joseph McAdam |
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Vol. 68 (1977), No. 1, 153–160
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Abstract |
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Let b,c be a system of parameters in a 2-dimensional local (Noetherian) domain (R,M). For n ≧ 0, the chain (bn : 1) ⊂ (bn : c) ⊂ (bn : c2) ⊂⋯ becomes stable. Thus define a function S(b,c,−) by letting S(b,c,n) be the least integer k ≧ 0 such that (bn : ck) = (bn : ck+1). Ratliff has shown that R is unmixed if and only if S(b,c,−) is bounded. This paper shows that if R is unmixed then for any 0≠d ∈ M there is an integer ∗d ≧ 0 such that for any system of parameters b,c and any i ≧ 0,S(b,c,∗b + i) = ∗c. |
Mathematical Subject Classification 2000
Primary: 13H99
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Milestones
Received: 1 June 1976
Published: 1 January 1977
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Authors |
| Stephen Joseph McAdam | |
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