A ring regular sequence for a module 
over a commutative unit
ring 
is a sequence 
of elements of 
such that,
for all 
, ..., 
,
1. Multiplication by 
is injective on 
.
2. 
.
If only condition (1) is fulfilled, the sequence is called weakly regular. When 
, a ring regular sequence is also called an 
-sequence or simply a regular sequence (Bruns and Herzog 1998).
