Discrete Valuation - Discrete Valuation Rings and Valuations On Fields

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:

    We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the child’s life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.
    Selma H. Fraiberg (20th century)

    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)

    Within the regions of the air,
    Compassed about with heavens fair,
    Great tracts of land there may be found
    Enriched with fields and fertile ground;
    Where many numerous hosts
    In those far distant coasts,
    For other great and glorious ends,
    Inhabit, my yet unknown friends.
    Thomas Traherne (1636–1674)