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Examples ofnoetherian
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It is possible to modify his approach, using anoetherianpartial ordering as before, and usingnoetherianinduction rather than transfinite induction.
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But it is interesting, because it does not a priori require such strong assumptions as to find anoetherianand confluent rewriting system.
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In particular, if isnoetherian, we see that any sequence of rewritings must eventually stop with an irreducible word.
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Therefore, is well-founded and anoetherianinduction on is possible.
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In the sequel we proceed bynoetherianinduction on this ordering.
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We prove the result bynoetherianinduction.
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Thus, we easily obtain that the restricted substitution rules arenoetherianand confluent, and we can apply the interpretation technique, through exactly the same steps as before.
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Anynoetherianscheme can be written uniquely as the union of finitely many maximal irreducible non-empty closed subsets, called its irreducible components.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Thus, a scheme isnoetherianif and only if it is locallynoetherianand quasi-compact.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It concerns a closed immersion of schemes (regular,noetherian) that is purely of codimension "d", and the relative local cohomology in the tale theory.
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This example is from Wikipedia and may be reused under a CC BY-SA license.More generally, a scheme is locallynoetherianif it is covered by spectra ofnoetherianrings.
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This example is from Wikipedia and may be reused under a CC BY-SA license.A locallynoetherianscheme is a locallynoetherianformal scheme in the canonical way: the formal completion along itself.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Practically allnoetherianrings that appear in application are catenary.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Noetherianmodules over arbitrary rings are always finitely generated.
From theCambridge English Corpus
Conversely, anoetherianintegrally closed domain is completely integrally closed.
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This example is from Wikipedia and may be reused under a CC BY-SA license.There are also equivalent conditions for non-noetherianintegral domains.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In other words, because infinite dimensional modules are not generally reflexive, the theory of dualities applies more easily to finitely generated algebras overnoetherianrings.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Dvissage is an adaptation of a certain kind ofnoetherianinduction.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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