Extension
If G arises as the group of units of a ring A, then an inner automorphism on G can be extended to a projectivity on the projective space over A by inversive ring geometry. In particular, the inner automorphisms of the classical linear groups can be so extended.
Read more about this topic: Inner Automorphism
Famous quotes containing the word extension:
“Where there is reverence there is fear, but there is not reverence everywhere that there is fear, because fear presumably has a wider extension than reverence.”
—Socrates (469399 B.C.)
“Slavery is founded in the selfishness of mans natureopposition to it, is [in?] his love of justice.... Repeal the Missouri compromiserepeal all compromisesrepeal the declaration of independencerepeal all past history, you still can not repeal human nature. It still will be the abundance of mans heart, that slavery extension is wrong; and out of the abundance of his heart, his mouth will continue to speak.”
—Abraham Lincoln (18091865)
“The medium is the message. This is merely to say that the personal and social consequences of any mediumthat is, of any extension of ourselvesresult from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.”
—Marshall McLuhan (19111980)