let be an A-algebra and let then there are 3 equivalent conditions:
i) is integral over A
ii)the subring generated by is finite over A (as an A-module?)
ii) an A-algebra such that and C is finite over A.
since y is integral then we know that there exists a monic polynomial s.t (*) but then the proof says is generated by , as an A-module.
To show this let
if then substracting times the relation (*) kills the leading term......I cannot get to this.... please help
how to show ?
can I just set ?? then and (every ring is a subring of itself right?)