Given a commutative unit ring 
, and an 
-module 
, a sequence 
of elements of 
is called a regular sequence for 
(or an 
-sequence for short), if, for all 
,
1. The multiplication by 
is injective on 
.
2. 
.
If only condition (1) is fulfilled, the sequence is called weakly regular. An 
-sequence is usually simply called a
regular sequence.
