A product of two or more non-trivial rings always has nonzero zero divisors: if x is an element of the product whose coordinates are all zero except pi&hairsp;(x) and y is an element of the product with all coordinates zero except pj&hairsp;(y) where i ≠ j, then xy = 0 in the product ring.
A product of two or more non-trivial rings always has nonzero zero divisors: if x is an element of the product whose coordinates are all zero except pi&hairsp;(x) and y is an element of the p.roduct with all coordinates zero except pj&hairsp;(y) where i ≠ j, then xy = 0 in the product ring