Notation used within "Prime ideal structure in commutative rings" by M. Hochster

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I was reading through this paper and I came across some rather confusing notation in the proof of Theorem 4. It says

Proof. ...$Y$ is finite, and it is clear that the image of the restriction of any element of $[b_1,b_2]$ to $d(b_1)\cup d(b_2)$ is the same as the image of its restriction to $Y$. Thus, we need only find $c\in I=(b_1,b_2)\cap[b_1,b_2]$ such that $c$ does not vanish on $Y$...

My question is what is the $[b_1,b_2]$ notation? My familiarity with its notation is as the Lie bracket, or perhaps the commutator. But neither of which make sense here since we want $I$ to be an ideal. Online searches have also yielded no help.

Any help is appreciated!