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Results tagged with noncommutative-rings
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user 90006
Questions about rings that are not necessarily commutative.
1
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Modification of nonfree locus
Let $ R $ be a commutative noetherian ring with identity. Let $ M $ be an $ R $-module. By definition the nonfree locus $ NF(M) $ of $ M $ is defined as the set of prime ideals $ {\mathfrak p} $ of $ …
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2
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Completion of an algebra
Based on arXiv:math/9802041v1, there is a definition for $NC$-filtration and $NC$-completion of an associated algebra over the complex numbers:
Let $R$ be an associative algebra and $R^{\rm Lie} = (R …
- 51
2
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0
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A version of Peskine and Szpiro's theorem in vanishing of local cohomology
C. Peskine and L. Szpiro in "Dimension projective finie et cohomologie locale",(Proposition 4.1) proved the following vanishing theorem for local cohomology:
Let$R$ be a regular local ring of charact …
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