Question: Solve using abelian group 32. Let R be a ring without identity. Let T be the set R X Z. Define addition and multiplication in

Solve using abelian group

32. Let R be a ring without identity. Let T be the set R X Z. Define addition and multiplication in 7' by these rules: | (7, m) + (s,n) = (r + 8, +n). (r, m)(s, n) = (rs + ms + nr, mn). (a) Prove that 7 is a ring with identity. (b) Let R consist of all elements of the form (r, 0) in T. Prove that R isa subring of T

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