divisor of zero

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If in a ring there are non-zero elements a and b such that ab=0, then a and b are divisors of zero. For example, in the ring of 2×2 real matrices,

and so each of the matrices on the left-hand side is a divisor of zero. In the ring Z6, consisting of the set {0, 1, 2, 3, 4, 5} with addition and multiplication modulo 6, the element 4 is a divisor of zero since 4.3=0.

Subjects: Mathematics.

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