Phrase guide

central simple algebra

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A finite-dimensional associative algebra over some field K that is a simple algebra and whose centre is exactly K.

Definition source: English Wiktionary via Wiktextract

Qualifier: ring theory

Topics: algebra, mathematics, sciences

Examples

  • The complex numbers #92;C form a central simple algebra over themselves, but not over the real numbers #92;R (the centre of #92;C is all of #92;C, not just #92;R). The quaternions #92;mathbbH form a 4-dimensional central simple algebra over #92;R.
  • The concept of central simple algebra over a field K represents a noncommutative analogue to that of extension field over K. In both cases, the object has no nontrivial two-sided ideals and has a distinguished field in its centre, although a central simple algebra need not be commutative and need not have inverses (does not have be a division algebra).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

7 source translations are retained for this English entry.

  • Dutch: centrale enkelvoudige algebra — type of associative algebra over a field
  • Dutch: CEA — type of associative algebra over a field
  • Polish: algebra centralna prosta — type of associative algebra over a field
  • Portuguese: álgebra simple central — type of associative algebra over a field
  • Portuguese: ASC — type of associative algebra over a field
  • Spanish: álgebra simple central — type of associative algebra over a field
  • Spanish: ASC — type of associative algebra over a field