Definition
Let and be two rings (they may or may not be commutative, or contain an identity), and let be a homomorphism. Suppose that is a module over . Then it can be regarded as a module over, if the action of is given via for and .
Read more about this topic: Restriction Of Scalars
Famous quotes containing the word definition:
“One definition of man is an intelligence served by organs.”
—Ralph Waldo Emerson (18031882)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lensif we are unaware that women even have a historywe live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (17721834)