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Wondering how to use Commutative in a sentence? Below are 10+ example sentences from authentic English texts. Including the meaning and synonyms such as independent.

Less frequent word

Commutative in a sentence

Commutative meaning

  1. Such that the order in which the operands are taken does not affect their image under the operation.
  2. Having a commutative operation.
  3. Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.

Synonyms of Commutative

independent

Related words

Other words often associated with Commutative or its synonyms:

autonomous breakaway free separatist autarkic unconditional fissiparous dependent

Using Commutative

  • The main meaning on this page is: Such that the order in which the operands are taken does not affect their image under the operation. | Having a commutative operation. | Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
  • Useful related words include: independent.
  • In the example corpus, commutative often appears in combinations such as: commutative ring, of commutative, commutative rings.

Context around Commutative

  • Average sentence length in these examples: 23.1 words
  • Position in the sentence: 8 start, 8 middle, 4 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

non 4× kaplansky 1× standard 1× noetherian 1×

Often after:

ring 6× rings 3× monoid 2× semigroup 2× algebra 2× group 1× elements 1× analogs 1× finite 1× hence 1×

Sentence patterns with Commutative

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

a commutative simple ring 1× a is commutative then the 1× a noetherian commutative ring 1× article is commutative algebra with 1× called a commutative monoid or 1× closer non commutative analog are 1× commutative monoid a 1× covering standard commutative algebra 1×

Sentence openings and endings

Common sentence openings:

a classic textbook 1× a closer non 1× a commutative simple 1× a full transitive 1× a group in 1× a least common 1×

Common sentence endings:

a commutative operation 1× an abelian monoid 1× another commutative semigroup 1× any r module 1× covariant hom functor 1× exactly the field 1×

Words around Commutative

Just before it in the word index:

commutations 16 commutation 45 commutating 2 commutated 16 commutable 3 communityworks 3

Just after it in the word index:

commutativity 12 commutator 18 commutators 9 commute 577 commuted 133 commuter 422

Similar in corpus frequency:

adrienne 123 airlift 123 alisson 123 anesthesia 123 antagonistic 123 asif 123

Corpus analysis for Commutative

  • In this selection, "commutative" usually appears near the start of the sentence. The average example has 23.1 words, and this corpus slice is mostly made up of statements.
  • Around the word, non, kaplansky, standard, ring, rings and monoid stand out and add context to how "commutative" is used.
  • Recognizable usage signals include a commutative simple ring and a is commutative then the. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "commutative" sits close to words such as adrienne, airlift and alisson, which helps place it inside the broader word index.

Example types with commutative

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

A classic textbook covering standard commutative algebra. (7 words)

Applications Let be a Noetherian commutative ring. (7 words)

I'd say "multiplication is a commutative operation. (8 words)

Longer example sentences

A least common multiple of a and b is a common multiple that is minimal in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one. (50 words)

A closer non-commutative analog are central simple algebras (CSAs) – ring extensions over a field, which are simple algebra (no non-trivial 2-sided ideals, just as for a field) and where the center of the ring is exactly the field. (41 words)

It may be noted that if one considers certain specific classes of matrices with non-commutative elements, then there are examples where one can define the determinant and prove linear algebra theorems that are very similar to their commutative analogs. (40 words)

Example sentences (20)

Commutative monoid A monoid whose operation is commutative is called a commutative monoid (or, less commonly, an abelian monoid).

If A is commutative then the center of A is equal to A, so that a commutative R-algebra can be defined simply as a homomorphism of commutative rings.

A group in which the group operation is not commutative is called a "non-abelian group" or "non-commutative group".

A typical counter to this argument comes directly from mathematics: While + is commutative on integers (and more generally any complex numbers), it is not commutative for other "types" of variable.

In 1921, Emmy Noether gave the modern axiomatic definition of (commutative) ring and developed the foundations of commutative ring theory in her paper Idealtheorie in Ringbereichen.

It can be shown that this definition is equivalent to the commutative one in commutative rings.

It may be noted that if one considers certain specific classes of matrices with non-commutative elements, then there are examples where one can define the determinant and prove linear algebra theorems that are very similar to their commutative analogs.

Kaplansky Commutative rings, p. 10, Ex 10. * In a commutative ring, an ideal maximal with respect to being not countably generated is prime.

Advertentie

There are no non-commutative finite division rings: Wedderburn's little theorem states that all finite division rings are commutative, hence finite fields.

Whenever we take the quotient of a commutative semigroup by a congruence, we get another commutative semigroup.

I'd say "multiplication is a commutative operation.

A classic textbook covering standard commutative algebra.

A closer non-commutative analog are central simple algebras (CSAs) – ring extensions over a field, which are simple algebra (no non-trivial 2-sided ideals, just as for a field) and where the center of the ring is exactly the field.

A commutative simple ring is precisely a field.

A full transitive closure is not needed; a commutative transitive closure and even weaker forms suffice.

A least common multiple of a and b is a common multiple that is minimal in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one.

An element in a commutative ring R may be thought of as an endomorphism of any R-module.

An ideal P satisfying the commutative definition of prime is sometimes called a completely prime ideal to distinguish it from other merely prime ideals in the ring.

A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud (1995), which uses "h A " to mean the covariant hom-functor.

Applications Let be a Noetherian commutative ring.

Advertentie

Common combinations with commutative

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "commutative" in a sentence?
An example: "Commutative monoid A monoid whose operation is commutative is called a commutative monoid (or, less commonly, an abelian monoid)." This page contains 10+ example sentences with the word "commutative" from authentic English texts.
What does "commutative" mean?
Commutative means: Such that the order in which the operands are taken does not affect their image under the operation.
What are synonyms of "commutative"?
Common synonyms of "commutative" include: independent.
How many example sentences with "commutative" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "commutative", drawn from a database of millions of English sentences.