Thread: modern alg

Let R be acommutative ring and let b be a fixed element of R. Prove that the set b = {r is in R and r = cb for some element c in R} is an ideal of R.

Originally Posted by wvlilgurl

Let R be acommutative ring and let b be a fixed element of R. Prove that the set b = {r is in R and r = cb for some element c in R} is an ideal of R.

Define . To show is an ideal of you need to show if then , and also that if then . These should be clear by definition.