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

Central Simple in a sentence

About this phrase

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

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

Other phrases with this word

Other phrases with simple:

day simple 20×

Other phrases with the same pattern

Same start:

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

Same ending:

day simple

Example types with central simple

Below, the examples are grouped by length and sentence type:

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.