discrete valuation ring वाक्य
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- A special case of this are the discrete valuation rings mentioned earlier.
- This says that KX is a discrete valuation ring with uniformizing parameter X.
- Of K, which is a discrete valuation ring.
- This is equivalent to the statement that any field or a discrete valuation ring.
- This is also a discrete valuation ring.
- Here is an example of a discrete valuation ring that is not a Japanese ring.
- George Mackey and Irving Kaplansky generalized Ulm's theorem to certain complete discrete valuation ring.
- I needed a valuation ring that is not a DVR and I assumed that made it a non-discrete valuation ring.
- Then " R " is a discrete valuation ring if and only if the maximal ideal of " R " is divisorial.
- In another joint work, Prasad and Yu determined all the quasi-reductive group schemes over a discrete valuation ring ( DVR ), [ 25 ].
- There is a similar construction with "'Z " "'p " replaced by any complete discrete valuation ring with finite uniformizer.
- Each such valuation ring is a discrete valuation ring and its maximal ideal is called a " place " of " K / k ".
- There is a similar construction with "'Z " "'p " replaced by any complete discrete valuation ring with finite residue class field.
- Just as a Dedekind domain is locally a discrete valuation ring, a Pr�fer domain is locally a valuation ring, so that Pr�fer domains act as non-noetherian analogues of Dedekind domains.
- Let the discrete valuation ring " R " be the ring of formal power series over " K " whose coefficients generate a finite extension of " k ".
- Definitely a field is a valuation ring and not a DVR, and is * way * simpler than any non-discrete valuation ring ( valuation ring with non-discrete value group ).
- A Cohen ring is a field or a complete characteristic zero discrete valuation ring whose maximal ideal is generated by a prime number " p " ( equal to the characteristic of the residue field ).
- A value group is called " discrete " if it is isomorphic to the additive group of the integers, and a valuation ring has a discrete valuation group if and only if it is a discrete valuation ring.
- Geometry of degeneration is largely then about the passage from generic to special fibers, or in other words how specialization of parameters affects matters . ( For a discrete valuation ring the topological space in question is the Sierpinski space of topologists.
- Arguing as in Example 3 . above and using the Zariski-Samuel theorem, it is easy to check that Hungerford's theorem is equivalent to the statement that any special principal ring is the quotient of a discrete valuation ring.
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