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