In the paper titled "Reducing Randomness via irrational numbers" by Chen & Kao (found here), while proving lemma 2.1 they state :
let $B_j$ be the field generated by $p_{1,1}, . . . , p_{1,k1}, . . . , p_{j,1}, . . . , p_{j,k_j}$ over $B_0$, where $B_0$ is a field of rational numbers and $p_{i,j}$'s are primes.
I donot understand how $B_j$ is an extension of $B_0$ since all the primes are already in $B_0$.
This appears to be a typo; from context it's clear that Chen and Kao intend to adjoin the square roots $\sqrt{p_{i,j}}$.