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for right regular.

Zero as a zero divisor

There is no need for a separate convention for the case , because the definition applies also in this case:
* If is a ring other than the zero ring, then is a (two-sided) zero divisor, because any nonzero element satisfies .
* If is the zero ring, in which , then is not a zero divisor, because there is no nonzero element that when multiplied by yields .

Some references include or exclude as a zero divisor in all rings by convention,

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