Local ring: Difference between revisions
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imported>Richard Pinch (supplied References Lang, section anchor Complete local ring) |
imported>Richard Pinch (→References: add page numbers for complete local ring) |
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==References== | ==References== | ||
* {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | pages=100 }} | * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55540-9 | pages=100,206-207 }} | ||
Revision as of 11:09, 21 December 2008
A ring is said to be a local ring if it has a unique maximal ideal . It is said to be semi-local if it has finitely many maximal ideals.
Complete local ring
A local ring A is complete if the intersection and A is complete with respect to the uniformity defined by the cosets of the powers of m.
References
- Serge Lang (1993). Algebra, 3rd ed. Addison-Wesley, 100,206-207. ISBN 0-201-55540-9.