(a)Show that S = {a+b √ 5 | a, b ∈ Q} is a subring of...

(a)Show that S = {a+b √ 5 | a, b ∈ Q} is a subring of the real numbers (with the usual + and × of real numbers). Explain why S is a field.

(b) Prove that if r is an element of a ring R and r 3 = 0, then 1 − r is a unit in R.

(c) Write down all the nilpotent elements of Z24, stating the index of nilpotence in each case. Verify the statement in part (b) holds in Z24.

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Expert Solution

Colby Messinger answered 1 year ago

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