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:
“I do not call the sod under my feet my country; but language–religion–government–blood–identity in these makes men of one country.”
—Samuel Taylor Coleridge (1772–1834)
“Unlike Boswell, whose Journals record a long and unrewarded search for a self, Johnson possessed a formidable one. His life in London—he arrived twenty-five years earlier than Boswell—turned out to be a long defense of the values of Augustan humanism against the pressures of other possibilities. In contrast to Boswell, Johnson possesses an identity not because he has gone in search of one, but because of his allegiance to a set of assumptions that he regards as objectively true.”
—Jeffrey Hart (b. 1930)
“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)