Let $x=(x_1,\ ...\ ,x_d)$ a system of parameters of local ring $(R,m)$.
We know that an $R$-algebra $B$ is called Cohen-Macaulay algebra if $x_{i+1}$ is a non-zero divisor in $(x_1,\ ...\ ,x_i)B$ for all $i$ and $B \neq (x_1,\ ...\ ,x_d)B$. But in a paper I saw a different definition: $(x_1,\ ...\ ,x_i)_{:B}x_{i+1}=(x_1,\ ...\ ,x_i)B$. It seems that the two definition is equivalent but I wonder what exactly the notation $(x_1,\ ...\ ,x_i)_{:B}$ means.
By the way, the second definition seems more convenient since the definition of almost Cohen-Macaulay only needs $\displaystyle\frac{(x_1,\ ...\ ,x_i)_{:B}x_{i+1}}{(x_1,\ ...\ ,x_i)B}$ to be almost zero.