Algebraically Closed Field

In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.

Read more about Algebraically Closed Field:  Examples, Equivalent Properties, Other Properties

Famous quotes containing the words closed and/or field:

    My old Father used to have a saying that “If you make a bad bargain, hug it the tighter”; and it occurs to me, that if the bargain you have just closed [marriage] can possibly be called a bad one, it is certainly the most pleasant one for applying that maxim to, which my fancy can, by any effort, picture.
    Abraham Lincoln (1809–1865)

    ... there are no chains so galling as the chains of ignorance—no fetters so binding as those that bind the soul, and exclude it from the vast field of useful and scientific knowledge. O, had I received the advantages of early education, my ideas would, ere now, have expanded far and wide; but, alas! I possess nothing but moral capability—no teachings but the teachings of the Holy Spirit.
    Maria Stewart (1803–1879)