A unit ring is a set together with two Binary Operators satisfying the following conditions:
Thus, a unit ring is a Ring with a multiplicative identity.
- 1. Additive associativity: For all ,
- 2. Additive commutativity: For all , ,
- 3. Additive identity: There exists an element such that for all
- 4. Additive inverse: For every , there exists a such that
- 5. Multiplicative associativity: For all ,
- 6. Multiplicative identity: There exists an element such that for all , ,
- 7. Left and right distributivity: For all ,
See also Binary Operator, Ring
Rosenfeld, A. An Introduction to Algebraic Structures. New York: Holden-Day, 1968.
© 1996-9 Eric W. Weisstein