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Suppose R {\displaystyle R} is a commutative unital ring, and x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} is a sequence of elements in R {\displaystyle R} . We say that the x i {\displaystyle x_{i}} s form a regular sequence in R {\displaystyle R} if the following are true:
The notion generalizes to that of regular sequence on a module.
is a commutative unital ring, and 
is a sequence of elements in . We say that the 
s form a regular sequence in if the following are true:
is not a zero divisor in 