Ring Theory
In ring theory an approximate identity is defined in a similar way, except that the ring is given the discrete topology so that a=aeλ for some λ.
A module over a ring with approximate identity is called non-degenerate if for every m in the module there is some λ with m=meλ.
Read more about this topic: Approximate Identity
Famous quotes containing the words ring and/or theory:
“When I received this [coronation] ring I solemnly bound myself in marriage to the realm; and it will be quite sufficient for the memorial of my name and for my glory, if, when I die, an inscription be engraved on a marble tomb, saying, “Here lieth Elizabeth, which reigned a virgin, and died a virgin.””
—Elizabeth I (1533–1603)
“The whole theory of modern education is radically unsound. Fortunately in England, at any rate, education produces no effect whatsoever. If it did, it would prove a serious danger to the upper classes, and probably lead to acts of violence in Grosvenor Square.”
—Oscar Wilde (1854–1900)