Ring Case
Given a ring R and a unit u in R, the map ƒ(x) = u−1xu is a ring automorphism of R. The ring automorphisms of this form are called inner automorphisms of R. They form a normal subgroup of the automorphism group of R.
Read more about this topic: Inner Automorphism
Famous quotes containing the words ring and/or case:
“What is a novel? I say: an invented story. At the same time a story which, though invented has the power to ring true. True to what? True to life as the reader knows life to be or, it may be, feels life to be. And I mean the adult, the grown-up reader. Such a reader has outgrown fairy tales, and we do not want the fantastic and the impossible. So I say to you that a novel must stand up to the adult tests of reality.”
—Elizabeth Bowen (1899–1973)
“In all unmerciful actions, the worst of men pay this compliment at least to humanity, as to endeavour to wear as much of the appearance of it, as the case will well let them.”
—Laurence Sterne (1713–1768)