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:

    Justice in the hands of the powerful is merely a governing system like any other. Why call it justice? Let us rather call it injustice, but of a sly effective order, based entirely on cruel knowledge of the resistance of the weak, their capacity for pain, humiliation and misery. Injustice sustained at the exact degree of necessary tension to turn the cogs of the huge machine-for- the-making-of-rich-men, without bursting the boiler.
    Georges Bernanos (1888–1948)

    The eloquence of one stimulates all the rest, some up to the speaking-point, and all others to a degree that makes them good receivers and conductors, and they avenge themselves for their enforced silence by increased loquacity on their return.
    Ralph Waldo Emerson (1803–1882)

    The planter, who is Man sent out into the field to gather food, is seldom cheered by any idea of the true dignity of his ministry. He sees his bushel and his cart, and nothing beyond, and sinks into the farmer, instead of Man on the farm.
    Ralph Waldo Emerson (1803–1882)

    We are now a nation of people in daily contact with strangers. Thanks to mass transportation, school administrators and teachers often live many miles from the neighborhood schoolhouse. They are no longer in daily informal contact with parents, ministers, and other institution leaders . . . [and are] no longer a natural extension of parental authority.
    James P. Comer (20th century)