In definitions when authors says if they mean if and only if.
Since everybody know therefore they write if insted of if and only if.
Suppose that R is a commutative ring and let I be an ideal of R. Suppose
that are such that there are positive integers with .
I basically need to know if it's true that , if not, give a counter example.
My working:
Given the definition of Ideals, then
I don't think the statement is true, since the definition isn't an if and only if implication, i.e it isn't necessarily true that given letting
Can someone please help me think of a counter example, or show me that i'm wrong. Thank you.