What does "with respect to the exclusion of a set" mean? I'm not good at English, but I'm studying math in English. Can anyone explain to me what is this sentence means? 


  Let $Q$ be an ideal maximal with respect to the exclusion of $T$. 


Thank you.
If you are studying multiplicative sets, it is probably in connection with this lemma:


  If $R$ is a commutative ring,  $T$ is a multiplicative subset$^\ast$ and $I$ is an ideal maximal with respect to exclusion of $T$, then $I$ is a prime ideal.


It means that $I$ has the property that if $J$ is another ideal properly containing $I$, then $J\cap T\neq \emptyset$.



$^\ast$ the definition ought to include the clause that $0\notin T\neq\emptyset$, of course
It is an ideal that is the largest without containing any elements of T. That is to say all other ideals that do not contain elements of T are subsets of Q.