The center of a ring is the set of elements that commute with every element in the ring. In other words, if you take an element from the center and multiply it by any element in the ring, the result is the same regardless of the order of multiplication. This concept is crucial for understanding the structure and properties of rings, especially in distinguishing between commutative and non-commutative rings, and it plays a significant role in examining ideal theory and module theory.
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