대한수학회논문집 (Communications of the Korean Mathematical Society)
- 제11권4호
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- Pages.887-893
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- 1996
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
ON CERTAIN GRADED RINGS WITH MINIMAL MULTIPLICITY
초록
Let (R,m) be a Cohen-Macaulay local ring with an infinite residue field and let $J = (a_1, \cdots, a_l)$ be a minimal reduction of an equimultiple ideal I of R. In this paper we shall prove that the following conditions are equivalent: (1) $I^2 = JI$. (2) $gr_I(R)/mgr_I(R)$ is Cohen-Macaulay with minimal multiplicity at its maximal homogeneous ideal N. (3) $N^2 = (a'_1, \cdots, a'_l)N$, where $a'_i$ denotes the images of $a_i$ in I/mI for $i = 1, \cdots, l$.