Approximate Identity - Ring Theory

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:

    Generally, about all perception, we can say that a sense is what has the power of receiving into itself the sensible forms of things without the matter, in the way in which a piece of wax takes on the impress of a signet ring without the iron or gold.
    Aristotle (384–323 B.C.)

    The great tragedy of science—the slaying of a beautiful theory by an ugly fact.
    Thomas Henry Huxley (1825–1895)