Let be a polynomial ring over some base field and
an ideal in . Denote by
,
the (sub-)ideal generated by the first elements of
. We obtain a chain of ideals

where each ideal differs from the preceeding by just one generator.
We may further assume that
.

Definition 3.1
An element is called -regular if does not represent
a zero divisor of . A sequence of elements
is called regular if each is -regular.