In abstract algebra, extension of scalars is a means of producing a module over a ring from a module over another ring, given a homomorphism between them. Intuitively, the new module admits multiplication by more scalars than the original one, hence the name extension.
Read more about Extension Of Scalars: Definition, Examples, Interpretation As A Functor, Connection With Restriction of Scalars
Famous quotes containing the words extension of and/or extension:
“The motive of science was the extension of man, on all sides, into Nature, till his hands should touch the stars, his eyes see through the earth, his ears understand the language of beast and bird, and the sense of the wind; and, through his sympathy, heaven and earth should talk with him. But that is not our science.”
—Ralph Waldo Emerson (1803–1882)
“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 (469–399 B.C.)