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Let A and B be ideals of R, such that:

A+B={a+b / a in A ,b in B}

AB={aibi / ai in A , bi in B}

A:B={x in R / xb in A} are all ideals of R

Show that A+B, AB, and A:B are ALL the ideals of R, where R is a commutative ring with identity 1.

Thanks guys