McCoy's Theorem

McCoy's theorem states that for a commutative algebraic structure, such as a ring, an element is a zero divisor if and only if there exists a non-zero element that, when multiplied by some power of the element's minimal polynomial, becomes zero. In simpler terms, it connects the idea of zero divisors (elements that can "cancel out" other non-zero elements through multiplication) to the algebraic polynomial relationships they satisfy. This theorem helps us understand the structure of algebraic systems by linking elements with certain polynomial properties to zero divisors.