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 and/or rings:
“One of the most highly valued functions of used parents these days is to be the villains of their children’s lives, the people the child blames for any shortcomings or disappointments. But if your identity comes from your parents’ failings, then you remain forever a member of the child generation, stuck and unable to move on to an adulthood in which you identify yourself in terms of what you do, not what has been done to you.”
—Frank Pittman (20th century)
“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)