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:
“Time has no divisions to mark its passage, there is never a thunderstorm or blare of trumpets to announce the beginning of a new month or year. Even when a new century begins it is only we mortals who ring bells and fire off pistols.”
—Thomas Mann (18751955)
“The theory [before the twentieth century] ... was that all the jobs in the world belonged by right to men, and that only men were by nature entitled to wages. If a woman earned money, outside domestic service, it was because some misfortune had deprived her of masculine protection.”
—Rheta Childe Dorr (18661948)