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Explore Artinian through 6 example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.

Rare word

Artinian in a sentence

Artinian meaning

  1. in which any descending chain of ideals eventually starts repeating.
  2. in which any descending chain of submodules eventually starts repeating.

Using Artinian

  • The main meaning on this page is: in which any descending chain of ideals eventually starts repeating. | in which any descending chain of submodules eventually starts repeating.
  • In the example corpus, artinian often appears in combinations such as: left artinian, artinian ring, is artinian.

Context around Artinian

  • Average sentence length in these examples: 15.8 words
  • Position in the sentence: 1 start, 4 middle, 1 end
  • Sentence types: 6 statements, 0 questions, 0 exclamations

Often before:

left 2×

Often after:

ring 2× integral 1× noetherian 1×

Sentence patterns with Artinian

These short patterns come directly from the example sentences and show how the word is often embedded:

a left artinian ring is 2× conversely every artinian integral domain 1× if right artinian 1× is not artinian 1× k is artinian if and 1× module is artinian noetherian projective 1×

Sentence openings and endings

Common sentence openings:

an algebra over 1× another consequence is 1× conversely every artinian 1× if the module 1× the integers however 1×

Common sentence endings:

a local ring 1× has finite dimension 1× hopkins levitzki theorem 1× if right artinian 1× is a field 1× is not artinian 1×

Words around Artinian

Just before it in the word index:

artin 5 artimus 2 artillerymen 9 artilleryman 5 artillery 1.308 artilects 2

Just after it in the word index:

artiodactyl 2 artiodactyla 4 artiodactyls 15 artis 24 artisan 300 artisanal 168

Similar in corpus frequency:

aaaaa 8 aage 8 aardvarks 8 abaca 8 abaji 8 abascal 8

Corpus analysis for Artinian

  • In this selection, "artinian" usually appears in the middle of the sentence. The average example has 15.8 words, and this corpus slice is mostly made up of statements.
  • Around the word, left, ring, integral and noetherian stand out and add context to how "artinian" is used.
  • Recognizable usage signals include a left artinian ring is and conversely every artinian integral domain. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "artinian" sits close to words such as aaaaa, aage and aardvarks, which helps place it inside the broader word index.

Example types with artinian

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Conversely, every Artinian integral domain is a field. (8 words)

The integers, however, form a Noetherian ring which is not Artinian. (11 words)

An algebra over a field k is artinian if and only if it has finite dimension. (16 words)

Longer example sentences

If the module is Artinian, Noetherian, projective or injective, then the endomorphism ring has a unique maximal ideal, so that it is a local ring. (25 words)

It is a somewhat surprising fact that a left Artinian ring is left Noetherian (the Hopkins–Levitzki theorem ). (18 words)

Another consequence is that a left Artinian ring is right Noetherian if and only if right Artinian. (17 words)

Example sentences (6)

Another consequence is that a left Artinian ring is right Noetherian if and only if right Artinian.

An algebra over a field k is artinian if and only if it has finite dimension.

Conversely, every Artinian integral domain is a field.

If the module is Artinian, Noetherian, projective or injective, then the endomorphism ring has a unique maximal ideal, so that it is a local ring.

It is a somewhat surprising fact that a left Artinian ring is left Noetherian (the Hopkins–Levitzki theorem ).

The integers, however, form a Noetherian ring which is not Artinian.

Common combinations with artinian

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "artinian" in a sentence?
An example: "Another consequence is that a left Artinian ring is right Noetherian if and only if right Artinian." This page contains 6 example sentences with the word "artinian" from authentic English texts.
What does "artinian" mean?
Artinian means: in which any descending chain of ideals eventually starts repeating.
How many example sentences with "artinian" are there?
Voorbeeldzinnen.info contains 6 example sentences with "artinian", drawn from a database of millions of English sentences.