### Rings and Proofs for Commutative Rings

(See attached file for full problem description with proper symbols) --- 1A) Let R be a commutative ring and let A = {t  R  tp = 0R} where p is a fixed element of R. Prove that if k, m  A and b  R, then both k + m and kb are in A. 1B) Let R be a commutative ring and let b be a fixed ele