Regular sequence in a ring

Definition

Suppose $R$ is a commutative unital ring, and $x_1,x_2,\dots ,x_n$ is a sequence of elements in $R$. We say that the $x_i$s form a regular sequence in $R$ if the following are true:

• $(x_1,x_2,\dots ,x_n)\ne R$
• $x_i$ is not a zero divisor in $R/(x_1,x_2,\dots ,x_{i-1})$

The notion generalizes to that of regular sequence on a module.