If a ring has zero divisors, is it necessarily commutative or non-commutative?
1 Answer
Aug 27, 2016
A ring can have zero divisors whether or not it is commutative.
Explanation:
Consider arithmetic modulo
This is a commutative ring with
The ring of
For example:
#((1,0),(0,0))((0,0),(0,1)) = ((0,0),(0,0))#
#((1,1),(0,0))((1,0),(0,0)) = ((1,0),(0,0)) != ((1,1),(0,0)) = ((1,0),(0,0))((1,1),(0,0))#