Solution Found!
Suppose that there is an integer n > 1 such that xn = x
Chapter 12, Problem 30E(choose chapter or problem)
QUESTION:
Suppose that there is an integer \(n > 1\) such that \(x^n\) = \(x\) for all elements \(x\) of some ring. If \(m\) is a positive integer and \(a^m\) = \(0\) for some \(a\), show that \(a\) = \(0\).
Questions & Answers
QUESTION:
Suppose that there is an integer \(n > 1\) such that \(x^n\) = \(x\) for all elements \(x\) of some ring. If \(m\) is a positive integer and \(a^m\) = \(0\) for some \(a\), show that \(a\) = \(0\).
ANSWER:
Step 1 of 4
Suppose there is an integer \(n > 1\) such that \(x^{n}=x\) for all x
The objective is to show that \(a = 0\). If \(a^{m} = 0\) for some \(a\) of ring \(R\), where \(m\) is a positive integer.