Regular sequence in a ring: Difference between revisions
(New page: ==Definition== Suppose <math>R</math> is a commutative unital ring, and <math>x_1, x_2, \ldots, x_n</math> is a sequence of elements in <math>R</math>. We say that the <math>x_i</math...) |
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* <math>x_i</math> is not a zero divisor in <math>R/(x_1,x_2,\ldots,x_{i-1})</math> | * <math>x_i</math> is not a zero divisor in <math>R/(x_1,x_2,\ldots,x_{i-1})</math> | ||
The notion generalizes to that of [[regular sequence | The notion generalizes to that of [[regular sequence on a module]]. | ||
Revision as of 14:08, 5 May 2008
Definition
Suppose 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
The notion generalizes to that of regular sequence on a module.