Examples of 'noetherian' in a sentence
Meaning of "noetherian"
Noetherian is an adjective used in mathematics to describe a type of ring that satisfies a specific ascending chain condition
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- Of a ring in which any ascending chain of ideals eventually starts repeating.
- Of a module in which any ascending chain of submodules eventually starts repeating.
- Alternative letter-case form of noetherian
How to use "noetherian" in a sentence
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noetherian
Dévissage is an adaptation of a certain kind of noetherian induction.
Practically all noetherian rings that appear in application are catenary.
We recall that it must also be noetherian.
Noetherian integrally closed domain.
Consequently we will only define locally noetherian formal schemes.
Noetherian topological space.
M has a composition series if and only if it is noetherian and artinian.
Being Noetherian is an extremely important finiteness condition.
The ring of algebraic integers is not Noetherian.
Every integrally closed noetherian domain is a Krull ring.
Any module that is finite as a set is Noetherian.
A Noetherian ring does not necessarily have a dualizing module.
A unique factorization domain is not necessarily a Noetherian ring.
Some standard terminology for Noetherian spaces will now be assumed.
Formal schemes are usually defined only in the Noetherian case.
See also
It is very hard to construct examples of Noetherian rings that are not universally catenary.
The chain condition also may be inherited by combinations or extensions of a Noetherian object.
Noetherian rings are named in honour of Emmy Noether.
A group such that all its subgroups are finitely generated is called Noetherian.
Any finitely generated right module over a right Noetherian ring is a Noetherian module.
All Noetherian rings are atomic.
The Weierstrass preparation theorem implies that rings of germs of holomorphic functions are Noetherian rings.
The spectrum of a Noetherian ring is a Noetherian space.
Every principal ideal domain is Noetherian.
A Noetherian local ring is Gorenstein if and only if its completion is Gorenstein.
Every localization of a commutative Noetherian ring is Noetherian.
Noetherian module A Noetherian module is a module such that every submodule is finitely generated.
The Krull dimension need not be finite even for a Noetherian ring.
A left Noetherian ring is left coherent and a left Noetherian domain is a left Ore domain.
Modules of finite uniform dimension generalize both Artinian modules and Noetherian modules.
Noetherian rings are named after Emmy Noether.
Semisimple rings are both Artinian and Noetherian.
It is right Noetherian but not left Noetherian.
Consequently, an irreducible ideal of a Noetherian ring is primary.
Noetherian rings of the following types are Cohen-Macaulay.
More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings.
Noetherian group, a group that satisfies the ascending chain condition on subgroups.
As mentioned above, such a ring can not be Noetherian.
Noetherian topological space, a topological space that satisfies the descending chain condition on closed sets.
However, the singular radical of a Noetherian ring is always nilpotent.
Is a scheme Noetherian if its topological space and its stalks are?
It has only been proven for special types of Noetherian rings, so far.
For Noetherian local rings, there is the following chain of inclusions.
The integers, considered as a module over the ring of integers, is a Noetherian module.
In a commutative Noetherian ring, there are only finitely many minimal prime ideals.
It has led to a better understanding of noncommutative rings, especially noncommutative Noetherian rings.
R is a Noetherian local domain whose maximal ideal is principal, and not a field.
In Chapter 4 we work on a quotient of a standard graded Noetherian algebra by homogeneous regular sequence.
A Noetherian ring is Cohen-Macaulay if and only if the unmixedness theorem holds for it.
The decomposition does not hold in general for non-commutative Noetherian rings.
