Question: Please solve it as fast as possible. Abstract Algebra 9. Let R be the ring Z50- (a) (3 PTS) Find an element of R which

Please solve it as fast as possible. Abstract Algebra

9. Let R be the ring Z50- (a) (3 PTS) Find an element of R which is a zero-divisor. (b) (3 PTS) Find an element of R which is a unit. (c) (3 PTS) Find an element of R, different from 0 and 1, which is idempotent. (An element a is called idempotent if a2 = a.) (d) (3 PTS) Find a nonzero element of R which is nilpotent. (An element a is called nilpotent if an = 0 for some positive integer n.)

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