Regular sequence in a ring

Definition
Suppose $$R$$ is a commutative unital ring, and $$x_1, x_2, \ldots, x_n$$ 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:


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

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