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noetherian condition - can I explain that Zariski in particular took local ring to be noetherian? This is however not the modern convention. It needs...

ring but a different presentation) is a better example?, which is more clearly a local ring. —- Taku (talk) I disagree that it is "more clearly local...

in which completion is deployed it to complete a Noetherian local ring (or just local ring, depending on your terminology) at its maximal ideal. In this...

to address the redirect Ring action. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 November 24#Ring action until a consensus...

should be taken before merging unit ring and unit (ring theory) : on one hand, a unit ring and a unit of a ring are different objects and merit IMHO...

seems to be missing in the sentence There is an example of a regular local ring A of dimension 1 and characteristic p>0 which is not excellent. If k is...

DVRs. Gene Ward Smith 21:26, 8 May 2006 (UTC) Isn't it true that the local ring at a point of an algebraic curve is a DVR iff the point is non-singular...

Ku-ring-gai has never been a "shire", it's always been a "council" (see the website, it says "ku-ring-gai council"). the "shire" term is not a generic...

semilocal, as the maximal ideals correspond to irreducible polynomials in the ring. There are infintely many of them (all the minimal polynomials of elements...

from turning rings into local rings? - 80.143.125.195 14:57, 18 January 2007 (UTC) I think the author has the wrong definition of "total ring of fractions...

are the materials of corona rings? It depends on corona rings design and manufacturing process. The custom corona rings are usually made from aluminium...

Image:ABBA - Ring Ring.ogg is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no...

term local ring here implicitly being used to refer to a local domain? If not, the definition of equicharacteristic in terms of the local ring and its...

of a ring R is its depth as a module over itself." With respect to what ideal? This should be with respect to the maximal ideal of a local ring, right...

as well. Local GAA team uses An Rinn, not Ring, local community development groups use An Rinn, not Ring, local schools use An Rinn, not Ring. The previous...

paragraph One can trace this back to the logical form of the definition of local ring. In a clean logical formulation, it can be put as 'for all r in R, either...

counterexample, let k be a field, and let k[x1, x2, x3, ...] be a polynomial ring over k in infinitely many indeterminates. Let J be the ideal (x1) + (x1,...

notion of "regular ring" does not have its own page!--129.70.14.128 21:03, 24 October 2007 (UTC) Serre's definition of a regular ring is not equivalent...

reference is: M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES, 36 (1969), 23-58. — Preceding unsigned comment added...

was one where the sheaf of holomorphic functions was normal, i.e. each local ring of holomorphic functions is normal. A necessary and sufficient condition...