Panther
发表于 2025-3-26 22:19:59
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墙壁
发表于 2025-3-27 01:14:15
0932-7134 following: If g = g f +. . . g f 1 1 r r is a linear combination of the f (with coe?cients g ? k), then we have i i 1 n V(f ,. . . ,f)= V(g,f ,. . . ,f ). Thus the set of solutions depends only on the ideal 1 r 1 r a? k gene978-3-8348-9722-0Series ISSN 0932-7134 Series E-ISSN 2512-7039
文艺
发表于 2025-3-27 05:46:16
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冲击力
发表于 2025-3-27 11:11:04
0932-7134 f systems of polynomial equations f (x ,. . . ,x )=0, 1 1 n . . . f (x ,. . . ,x )=0. r 1 n Here the f ? k are polynomials in n variables with coe?cients in a ?eld k. i 1 n n ThesetofsolutionsisasubsetV(f ,. . . ,f)ofk . Polynomialequationsareomnipresent 1 r inandoutsidemathematics,and
哺乳动物
发表于 2025-3-27 15:45:59
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不如屎壳郎
发表于 2025-3-27 20:44:18
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Desert
发表于 2025-3-28 00:08:14
Integration and Demonstrations, simple situations, the converse to this statement is true, see Proposition 14.14, Theorem 14.32 and Theorem 14.126 below. One could say that flatness is the correct generalization of this naive point of view to the general case.
committed
发表于 2025-3-28 04:30:03
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友好
发表于 2025-3-28 10:02:48
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jumble
发表于 2025-3-28 11:16:53
Flat morphisms and dimension, simple situations, the converse to this statement is true, see Proposition 14.14, Theorem 14.32 and Theorem 14.126 below. One could say that flatness is the correct generalization of this naive point of view to the general case.