A finite ring is a ring that contains a finite number of elements. In abstract algebra, a ring is defined as a set equipped with two binary operations: addition and multiplication, which satisfy certain properties. Specifically, a ring must satisfy the following axioms: 1. **Additive Identity**: There exists an element \(0\) such that \(a + 0 = a\) for all elements \(a\) in the ring.
A Galois ring is a type of algebraic structure related to the field of Galois theory and finite fields. It generalizes the concept of a finite field and is particularly useful in coding theory and other areas of mathematics.
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