Below you will find example sentences with "central simple". The examples show how this phrase is used in natural context and which words often surround it.

Central Simple in a sentence

Corpus data

  • Displayed example sentences: 6
  • Discovered as a combination around: simple
  • Corpus frequency in the collocation scan: 4
  • Phrase length: 2 words
  • Average sentence length: 28.3 words

Words in this phrase

central simple

Meanings of words in this phrase

  • central can mean: Being in the centre. Common word
  • simple can mean: Uncomplicated; lacking complexity; taken by itself, with nothing added. Frequent word

Sentence profile

  • Phrase position: 2 start, 3 middle, 1 end
  • Sentence types: 6 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

a central simple algebra over 1× analog are central simple algebras csas 1× are a central simple algebra over 1× example the central simple algebras over 1× is a central simple algebra over 1× of a central simple algebra is 1× section a central simple algebra is 1×

Sentence openings and endings

Common sentence openings:

a central simple 1× a closer non 1× for example the 1× in this section 1× since the center 1× the skolem noether 1×

Common sentence endings:

or the quaternions 2× algebra is inner 1× exactly the field 1× have finite dimension 1× over its center 1×

Context words

These words often appear near this phrase in the example sentences:

algebra 10× field 5× reals 5× center 4× finite 3× algebras 3× quaternions 3× matrix 2× example 2× non 2× csas 2× ring 2×

Related phrases

day simple simple moving central bank central banks central america central asia central oregon european central simple majority central florida

Phrases around this combination

Other phrases discovered around simple:

day simple 20×

Just before it in the phrase index:

central railway central park central pacific central oregon central michigan central maine

Just after it in the phrase index:

centres across centuries ago century fox ceo douglas ceo jim ceo mark

Other phrases with the same pattern

Same start:

central bank central banks central america central asia central oregon central florida

Same ending:

day simple

Corpus analysis

  • The phrase "central simple" has 2 words and usually appears in the middle in these examples. The average sentence has 28.3 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as a central simple algebra over, analog are central simple algebras csas, algebra, field and reals stand out.
  • In the phrase index, this combination connects with day simple, simple moving, central bank and day simple, linking the page to nearby combinations.

Example types with central simple

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

In this section, a central simple algebra is assumed to have finite dimension. (13 words)

The Skolem–Noether theorem states any automorphism of a central simple algebra is inner. (14 words)

Since the center of a simple k-algebra is a field, any simple k-algebra is a central simple algebra over its center. (23 words)

Longer example sentences

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)

For example, the only finite field extension of the real numbers is the complex numbers, while the quaternions are a central simple algebra over the reals, and all CSAs over the reals are Brauer equivalent to the reals or the quaternions. (41 words)

A central simple algebra over K is a matrix algebra over a (finite dimensional) division algebra with center K. For example, the central simple algebras over the reals are matrix algebras over either the reals or the quaternions. (38 words)

Example sentences (6)

Since the center of a simple k-algebra is a field, any simple k-algebra is a central simple algebra over its center.

A central simple algebra over K is a matrix algebra over a (finite dimensional) division algebra with center K. For example, the central simple algebras over the reals are matrix algebras over either the reals or the quaternions.

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.

For example, the only finite field extension of the real numbers is the complex numbers, while the quaternions are a central simple algebra over the reals, and all CSAs over the reals are Brauer equivalent to the reals or the quaternions.

In this section, a central simple algebra is assumed to have finite dimension.

The Skolem–Noether theorem states any automorphism of a central simple algebra is inner.