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)
“You held my hand
and were instant to explain
the three rings of danger.”
—Anne Sexton (1928–1974)
“... my one aim and concentrated purpose shall be and is to show that women can learn, can reason, can compete with men in the grand fields of literature and science ... that a woman can be a woman and a true one without having all her time engrossed by dress and society.”
—M. Carey Thomas (1857–1935)