| 1. | A special case of this are the discrete valuation rings mentioned earlier.
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| 2. | This says that KX is a discrete valuation ring with uniformizing parameter X.
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| 3. | Of K, which is a discrete valuation ring.
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| 4. | This is equivalent to the statement that any field or a discrete valuation ring.
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| 5. | This is also a discrete valuation ring.
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| 6. | Here is an example of a discrete valuation ring that is not a Japanese ring.
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| 7. | George Mackey and Irving Kaplansky generalized Ulm's theorem to certain complete discrete valuation ring.
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| 8. | I needed a valuation ring that is not a DVR and I assumed that made it a non-discrete valuation ring.
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| 9. | Then " R " is a discrete valuation ring if and only if the maximal ideal of " R " is divisorial.
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| 10. | In another joint work, Prasad and Yu determined all the quasi-reductive group schemes over a discrete valuation ring ( DVR ), [ 25 ].
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