"Unit" Versus "Ring With Unit"
In ring theory, in a given ring R any element with a multiplicative inverse is called a unit of the ring, i.e., the term may refer to any invertible element, not only the unit element 1R. The term ring with a unit is nevertheless well-defined, because in order to define the notion of invertible, the ring must have a unit element 1R. Thus, a ring with "any" unit is always a unital ring.
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Famous quotes containing the words unit and/or ring:
“During the Suffragette revolt of 1913 I ... [urged] that what was needed was not the vote, but a constitutional amendment enacting that all representative bodies shall consist of women and men in equal numbers, whether elected or nominated or coopted or registered or picked up in the street like a coroner’s jury. In the case of elected bodies the only way of effecting this is by the Coupled Vote. The representative unit must not be a man or a woman but a man and a woman.”
—George Bernard Shaw (1856–1950)
“Generally, about all perception, we can say that a sense is what has the power of receiving into itself the sensible forms of things without the matter, in the way in which a piece of wax takes on the impress of a signet ring without the iron or gold.”
—Aristotle (384–323 B.C.)