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Examples ofartinian
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An algebra over a field "k" isartinianif and only if it has finite dimension.
From
This example is from Wikipedia and may be reused under a CC BY-SA license.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Artinianserial ring structure is classified in cases depending on the quiver structure.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Rings such as the ring of integers are semiprimitive, and anartiniansemiprimitive ring is just a semisimple ring.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.In a rightartinianring, any nil ideal is nilpotent.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.A ring is semisimple if and only if it isartinianand is semiprimitive.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
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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