Question

which elements of ZxZ are zero divisors ?

Answer 1

Definition of zero divisor:A non-zero Elements a & b of a ring are said to be zero divisor,if

a.b=0

Here, (m,0) and (0,n) are non-zero elements of ring Z×Z,for any non-zero m,n belong to Z(m and n not necessarily distinct) But

(m,0).(0,n)={(m).(0),(0).(n)}

=(0,0)

Here, (m,0) and (0,n) are zero divisor of ring Z×Z, For any non-zero value of m and n.

Hence ,There are infinitely many zero divisors in Z×Z.