A unit ring is a set together with two Binary Operators satisfying the following conditions:

- 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 , and .

**References**

Rosenfeld, A. *An Introduction to Algebraic Structures.* New York: Holden-Day, 1968.

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1999-05-26