Namespaces
Variants
Actions

Uniformizing element

From Encyclopedia of Mathematics
Revision as of 17:20, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

An element of a discrete valuation ring (cf. Discretely-normed ring) with prime ideal such that . If are two uniformizing elements in , then the element is invertible in . Let be a system of representatives in for the elements of the residue field . Then any element can be uniquely expressed as a power series , where and is a uniformizing element. If the ring is complete relative to the discrete valuation, then any power series of the above form represents an element .

If is the local ring of functions at a simple point of an algebraic curve , then is a uniformizing element if and only if has a zero of order one at .


Comments

References

[a1] E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9
How to Cite This Entry:
Uniformizing element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Uniformizing_element&oldid=33282
This article was adapted from an original article by L.V. Kuz'min (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article