Let $A\subset B$ be commutative rings with unit. Is there any standard notation for the integral closure of $B$ over $A$? I can't find any, not on the internet, nor on any algebraic number theory books I know. I find it to be absolutely horrible to write "and $A'$ be the integral closure of $B$ over $A$" every time I need it. Therefore, a notation would be convenient.
If there are none, what do you think of this one? $$\mathfrak{C}(B/A)$$ it is elegant, the $\mathfrak{C}$ stands for $closure$, which is the right word in both English and French, and I didn't find this notation anywhere else. Also, we can recycle it in $$\mathfrak{C}(A)$$ to denote the integral closure of $\mathrm{Frac}(A)$ over $A$.
However, it is very different to the notation $$\mathcal{O}_K,$$ where $K$ is a number field, and we can clearly not use the notation $\mathcal{C}(A/B)$ for our purposes.
I would love to hear your suggestions, remarks, and anything you would have to say. Thanks.
EDIT #1: Maybe $$\mathfrak{C}_1(B/A)$$ would be nice, it is quite visual and the $1$ reminds us that we are interested in unitary polynomials.