Detailed solutions please 2 Let R be a commutative ring and

Detailed solutions please: 2. Let R be a commutative ring and let r, s and r be elements of R with r not equal to OR? Prove that if sr = rt, then either s = t or r is a zero divisor of R.

Solution

its given that r,s and t are the elements of the commutative ring R

and rs=rt   [given]

there the condition that r not = 0

so if r can\'t be zero then

inorder to hold the equation rs=rt as true

we need s = t

or another possiblity could be that the element r is a divisor of R that is

r goes into R some integral number of times.

Hence if sr = rt

we either need

s = t or r be a zero divisor of R