Let (a,b) is a zero-divisor in
Since (a,b) is zero-divisor, there exists (c,d) in
Since
Also,
Conversely:
Let a and b are zero divisors.
Since a is zero divisor,there exist element
Also, b is zero divisor, there exist element
Hence, for
By definition (a,b) is zero diisor in
Hence, proved
and are isomorphic
x=-3
Let U and W be vector spaces over a field K. Let V be the set of ordered pairs (u,w) where
(This space V is called the external direct product of U and W.)