Question: Let R be a ring, and let a be a fixed element of R. Let R a be the subring of R that is the

Let R be a ring, and let a be a fixed element of R. Let R_a be the subring of R that is the intersection of all subrings of R containing a. The ring R_a is the subring of R generated by a. Show that the abelian group (R_a,+) is generated (in the sense of Section 7) by {aⁿ |n ∈ Z⁺}.

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