Answer to Question #87225 in Abstract Algebra for Deepanshi

Question

a) Consider the ring R= Z(subscript)3[x] / < x^8 - 1>
i) Is R a finite ring?
ii) Does R have zero divisors?
iii) Does R have nilpotent elements?
Give reasons for your answers.
b) Give an example, with justification, of a subset of a ring that is a subgroup under
addition but not a subring.
c) Construct a multiplication (Cayley) table for 3Z/9Z.

Answer 1

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