Non-commutative local rings arise naturally as endomorphism rings in the study of length and is indecomposable, then its endomorphism ring is local.
42.
Taking the completion is a minor technical complication caused by the fact that not all local rings are quotients of regular ones.
43.
In particular if " R " is an Artinian local ring then the Matlis module is the same as the dualizing module.
44.
At a foundational level we must use the second style of definition, to describe what a local ring means in a category.
45.
Police arrested a local ring of drug traffickers and seized 107 bags of heroin, the news agency said, but gave no other details.
46.
A local complete intersection ring is a completion is the quotient of a regular local ring by an ideal generated by a regular sequence.
47.
Local ring expert and sports columnist Joaquin Henson blamed the high incidence of boxing-related deaths and injuries to negligient sports officials, who allow mismatches.
48.
A local family court judge required him to enroll in the neighborhood Police Athletic League and take his right hook to the local ring.
49.
An equivalent definition in terms of commutative algebra may be given, which extends to local ring at this point is not a regular local ring.
50.
An equivalent definition in terms of commutative algebra may be given, which extends to local ring at this point is not a regular local ring.
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