Show that, in a domain, every associate of an atom is an atom.
An atom is the same thing as an irreducible element.
I think these two facts will be important to prove this statement:
A nonunit is an atom if and only if it cannot be written as a product of two nonzero nonunits
Two elements are associates if and only if one is a unit multiple of the other.
I just need help with the actual proof writing. I don't know how to convert this information into a nice flowing proof. Any advice would be appreciated!
I'm also a little confused because of this link Irreducible elements are not associates