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The Prime Spectrum of Commutative Differential Algebras

โœ Scribed by J.J. Moloney

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
187 KB
Volume
133
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

For a commutative differential algebra., , if (p_{1}) and (p_{2}) are prime ideals with (p_{1} \subset p_{2}, p_{1} \neq p_{2}), and (D\left(p_{1}\right)) not contained in (p_{2}), then there exists a prime ideal (p_{3} \subset p_{2}), with (p_{3} \not p_{1}) and (p_{1} \not p_{3}) and (\left{x \mid D^{k} x \in p_{1}\right.) for all (\left.k \geqslant 0\right} \subset p_{3}). This yields an alternative proof that there is no non-trivial derivation on (C^{k}([0,1])) and gives a generalized existence theorem for polarized prime ideals of (C^{2}([0,1], C)).

ic 1995 Academic Press. Inc.

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