Discrete Valuation Rings and Valuations On Fields
To every field with discrete valuation we can associate the subring
of, which is a discrete valuation ring. Conversely, the valuation on a discrete valuation ring can be extended to a valuation on the quotient field giving a discrete valued field, whose associated discrete valuation ring is just .
Read more about this topic: Discrete Valuation
Famous quotes containing the words discrete, rings and/or fields:
“One can describe a landscape in many different words and sentences, but one would not normally cut up a picture of a landscape and rearrange it in different patterns in order to describe it in different ways. Because a photograph is not composed of discrete units strung out in a linear row of meaningful pieces, we do not understand it by looking at one element after another in a set sequence. The photograph is understood in one act of seeing; it is perceived in a gestalt.”
—Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)
“Ah, Christ, I love you rings to the wild sky
And I must think a little of the past:
When I was ten I told a stinking lie
That got a black boy whipped....”
—Allen Tate (1899–1979)
“Is America a land of God where saints abide for ever? Where golden fields spread fair and broad, where flows the crystal river? Certainly not flush with saints, and a good thing, too, for the saints sent buzzing into man’s ken now are but poor- mouthed ecclesiastical film stars and cliché-shouting publicity agents.
Their little knowledge bringing them nearer to their ignorance,
Ignorance bringing them nearer to death,
But nearness to death no nearer to God.”
—Sean O’Casey (1884–1964)