Identity in Rings
According to the glossary of ring theory, convention assumes the existence of a multiplicative identity for any ring. With this assumption, all rings are unital, and all ring homomorphisms are unital, and (associative) algebras are unital iff they are rings. Authors who do not require rings to have identity will refer to rings which do have identity as unital rings, and modules over these rings for which the ring identity acts as an identity on the module as unital modules or unitary modules.
Read more about this topic: Unital Algebra
Famous quotes containing the words identity in, identity and/or rings:
“When I quit working, I lost all sense of identity in about fifteen minutes.”
—Paige Rense (b. 1929)
“I look for the new Teacher that shall follow so far those shining laws that he shall see them come full circle; shall see their rounding complete grace; shall see the world to be the mirror of the soul; shall see the identity of the law of gravitation with purity of the heart; and shall show that the Ought, that Duty, is one thing with Science, with Beauty, and with Joy.”
—Ralph Waldo Emerson (1803–1882)
“It is told that some divorcees, elated by their freedom, pause on leaving the courthouse to kiss a front pillar, or even walk to the Truckee to hurl their wedding rings into the river; but boys who recover the rings declare they are of the dime-store variety, and accuse the throwers of fraudulent practices.”
—Administration in the State of Neva, U.S. public relief program. Nevada: A Guide to the Silver State (The WPA Guide to Nevada)