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- System_of_parameters abstract "In commutative algebra, a system of parameters for a local ring of Krull dimension d with maximal ideal m is a set of elements x1, ..., xd that satisfies any of the following equivalent conditions: m is a minimal prime of (x1, ..., xd). The radical of (x1, ..., xd) is m. Some power of m is contained in (x1, ..., xd). (x1, ..., xd) is m-primary.Every local Noetherian ring admits a system of parameters.It is not possible for fewer than d elements to generate an ideal whose radical is m because then the dimension of R would be less than d.If M is a k-dimensional module over a local ring, then x1, ..., xk is a system of parameters for M if the length of M / (x1, ..., xk)M is finite.".
- System_of_parameters wikiPageID "30823935".
- System_of_parameters wikiPageRevisionID "413417694".
- System_of_parameters hasPhotoCollection System_of_parameters.
- System_of_parameters subject Category:Commutative_algebra.
- System_of_parameters comment "In commutative algebra, a system of parameters for a local ring of Krull dimension d with maximal ideal m is a set of elements x1, ..., xd that satisfies any of the following equivalent conditions: m is a minimal prime of (x1, ..., xd). The radical of (x1, ..., xd) is m. Some power of m is contained in (x1, ..., xd).".
- System_of_parameters label "System of parameters".
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- System_of_parameters sameAs Q7663733.
- System_of_parameters sameAs Q7663733.
- System_of_parameters wasDerivedFrom System_of_parameters?oldid=413417694.
- System_of_parameters isPrimaryTopicOf System_of_parameters.