Degree (mathematics) - Degree of A Field Extension

Degree of A Field Extension

Given a field extension K/F, the field K can be considered as a vector space over the field F. The dimension of this vector space is the degree of the extension and is denoted by .

Read more about this topic:  Degree (mathematics)

Famous quotes containing the words degree of, degree, field and/or extension:

    It is true that genius takes its rise out of the mountains of rectitude; that all beauty and power which men covet are somehow born out of that Alpine district; that any extraordinary degree of beauty in man or woman involves a moral charm.
    Ralph Waldo Emerson (1803–1882)

    A certain degree of ceremony is a necessary outwork of manners, as well as of religion; it keeps the forward and petulant at a proper distance, and is a very small restraint to the sensible and to the well-bred part of the world.
    Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

    I would say that deconstruction is affirmation rather than questioning, in a sense which is not positive: I would distinguish between the positive, or positions, and affirmations. I think that deconstruction is affirmative rather than questioning: this affirmation goes through some radical questioning, but it is not questioning in the field of analysis.
    Jacques Derrida (b. 1930)

    The desert is a natural extension of the inner silence of the body. If humanity’s language, technology, and buildings are an extension of its constructive faculties, the desert alone is an extension of its capacity for absence, the ideal schema of humanity’s disappearance.
    Jean Baudrillard (b. 1929)