A unit ring is a ring with a multiplicative identity. It is therefore sometimes also known as a "ring with identity." It is given by a set together with two binary operators S(+, *) satisfying the following conditions: 1. Additive associativity: For all a, b, c element S, (a + b) + c = a + (b + c), 2. Additive commutativity: For all a, b element S, a + b = b + a, 3.
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