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Homework Statement
In a ring with multiplicative identity, If x^n is in an ideal then is x also in the ideal? with n a natural number.
The Attempt at a Solution
I can't find a proof. Which is likely to mean the statement is false?
I can't find a proof. Which is likely to mean the statement is false?
Good point. An example might be the ideal <2^2> in N which contains no element 2.It is perfectly possible for the ideal generated by x^2 to have x in it. It is just not *certain* to have x in it.