Examples of 'local ring' in a sentence
Meaning of "local ring"
local ring - In telecommunication, a local ring refers to a network topology where end-user devices or terminals are connected in a circular or ring-like configuration within a limited geographic area. It enables data transmission and communication between nearby nodes efficiently
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- A commutative ring with a unique maximal ideal, or a noncommutative ring with a unique maximal left ideal or (equivalently) a unique maximal right ideal.
- The non-routing segment of a token ring network.
How to use "local ring" in a sentence
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local ring
A regular local ring is an example of such a ring.
The completion of a regular local ring is regular.
A local ring that is an integral domain is called a local domain.
A projective module over a local ring is free.
The local ring of a normal point of a variety is analytically normal.
Every localization of a regular local ring is regular.
Local ring net.
The zero ring is not a local ring.
He was sold to a local ring of flesh peddlers.
Any such subring will be a local ring.
The filtration of a local ring by the powers of its maximal ideal.
Every field is a regular local ring.
The local ring in question is then the carrier of the formal moduli.
Artinian local ring.
A module is said to be strongly indecomposable if its endomorphism ring is a local ring.
See also
The dual numbers form a local ring since there is a unique maximal ideal.
A nonzero ring in which every element is either a unit or nilpotent is a local ring.
The English term local ring is due to Zariski.
In turn this implies that the localization of a regular local ring is regular.
Then R is a finite local ring which is not principal.
Every field is a Henselian local ring.
An Artinian local ring is complete.
A valuation ring OO is a local ring.
A local ring announcer was used instead of the usual Bruce Buffer.
A is a regular local ring.
A Noetherian local ring is Gorenstein if and only if its completion is Gorenstein.
In particular, every valuation ring is a local ring.
A regular local ring is an example of a Cohen-Macaulay ring.
In particular, it is a regular local ring of dimension n.
Jumping numbers of a simple complete ideal in a two-dimensional regular local ring.
Any quasi-excellent reduced local ring is analytically reduced.
A theorem of Kaplansky states “ every projective module over a local ring is free ”.
Every Cohen-Macaulay local ring is a Buchsbaum ring.
The Auslander-Buchsbaum theorem states that every regular local ring is a UFD.
A Noetherian local ring is called a Cohen-Macaulay ring if its dimension is equal to its depth.
All but the youngest son . He was sold to a local ring of flesh peddlers.
The category of finitely-generated modules over a finite R-algebra, where R is a commutative Noetherian complete local ring.
More generally, let R be a regular local ring with maximal ideal m.
In particular, the endomorphism ring of M is a commutative local ring.
In the local ring case, it does matter.
In mathematics, a Henselian ring ( or Hensel ring ) is a local ring in which Hensel 's lemma holds.
For an element x of the local ring R, the following are equivalent,.
In fact, a regular local ring is a UFD.
We also write ( R, m ) for a commutative local ring R with maximal ideal m.
Well, I have a local ring guy.
Replacing A by a localization, we can assume A is a local ring with maximal ideal p {\displaystyle {\mathfrak {p.
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Examples of using Ring
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And place a ring upon her hand
Ring tones will not hold up in court
I had to go into the ring to finish it myself
Examples of using Local
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I called the local disposal service in town
Local fodder production was encouraged instead of importing
Activities in local areas and holiday centres
