Talk:Element of Integral Domain Divides Zero

zero divisor

An integral domain has no proper zero divisors by definition. It seems that a divisor of zero and a zero divisor are different. --Fake Proof (T C) 10:50, 9 April 2023 (UTC)

Yes that is true. A zero divisor, a.k.a. a divisor of zero is an element defined as such on that page.

On the other hand, in the context of general divisibility, every element can be said to trivially "divide" zero, because zero is a multiple of every number -- zero is the factor to multiply it by.

Hence the way to think about it is to consider the term zero divisor as a specialised piece of jargon that means what it is defined to mean, and does not mean a factor of zero which gets you zero by multiplying it by zero. --prime mover (talk) 07:22, 19 April 2023 (UTC)

See Definition:Zero Divisor/Warning --prime mover (talk) 09:33, 19 April 2023 (UTC)