In Hulek's Elementary Algebraic Geometry, Nakayama's lemma is stated as follows: Let $A \neq 0$ be a finite $B$-algebra. Then for all proper ideals $m$ of $B$, we have $mA \neq A$. (Here, $A$ and $B$ are both commutative rings with identity.) My question is: how is that related to the usual statements, e.g. Statement 1 in wikipedia: http://en.wikipedia.org/wiki/Nakayama_lemma#Statement? Specifically, does the wikipedia statement imply Hulek's, and if so, how?
Edit: While the statement is cited correctly, it is misleading, because Hulek's definition of what it means for $A$ to be a finite $B$-algebra is that (1) $B\subset A$ is a subring, and (2) there are $a_i \in A$ such that $A=Ba_1+\cdots+Ba_n$.