Let R be a ring and fix b ∈R. (a) Show that S = {n1R ∈R : n ∈Z } is a subring of R. (b) Show that T = {rb ∈R : r ∈R } is a subring of R. (c) Is M = {nb ∈R : n ∈Z } always a subring of R? If no, give a counterexample. If yes, prove it. (Note this is slightly different from the sets in parts (a) and (b).)1

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