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Consider p and q be any nonzero element of R.
With no zero divisiors,
and if the pq+pq+pq+...m×=m⋅(pq)
with no zero divisors, , m⋅q=0
If a is an idempotent in a commutative ring, show that 1−a is also an idempotent.
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Let × be a binary operation on set of rational number Q defined as follows: a⋅b=a+b+2ab, where a,b∈Q
a) Prove that × is commutative, associate algebraic operation on Q
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