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- W2024809923 abstract "and dimension d. The most primitive quantities attached to an ideal Z are its height, ht(Z), and its minimum number of generators, u(Z). The fundamental relation between ht(Z) and u(Z) is pro- vided by Krull’s theorem: (1) u(Z) > ht(Z). The case of equality is noteworthy enough and Z will be called a complete intersec- tion if it so happens. (Strictly, this terminology is used when the ideal is generated by a regular sequence, but the two notions coincide in what will be our standard con- text - that of Cohen-Macaulay rings.) To bridge the gap between o(Z) and ht(Z) several other measures have been in- troduced. We single out: (i) ara(Z) = arithmetical rank of Z : = the least integer I such that the radical of Z is the radical of an r-generated ideal. (ii) I(Z) = analytic spread of Z := Krull dimension of the algebra @I’@" @default.
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- W2024809923 date "1985-11-01" @default.
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- W2024809923 title "The complete intersection locus of certain ideals" @default.
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- W2024809923 doi "https://doi.org/10.1016/0022-4049(85)90023-4" @default.
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