central simple algebra
central simple algebra noun: a finite-dimensional associative algebra over some field K that is a simple algebra and whose centre is exactly K.
Noun
central simple algebra (plural central simple algebras)
- A finite-dimensional associative algebra over some field K that is a simple algebra and whose centre is exactly K.
- 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...
- Synonyms:
- CSA
central simple algebra meaning in Tamil
central simple algebra in Tamil
- மைய எளிய இயற்கணிதம்
Examples of central simple algebra in a sentence
- This crossed product E#92;alphaG was introduced by Noether and played a significant role in the classical theory of central simple algebras.1987, Gregory Karpilovsky, The Algebraic Structure of Crossed Products, Elsevier (North-Holland), page 151:
- Let A#95;1,A#95;2 be central simple algebras over a field K.2014, Jörg Jahnel, Brauer Groups, Tamagawa Measures, and Rational Points on Algebraic Varieties, American Mathematical Society, page 84:
Synonyms of central simple algebra
Forms of central simple algebra
| plural | central simple algebras |
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Questions about central simple algebra
- What does central simple algebra mean?
- Central simple algebra means a finite-dimensional associative algebra over some field K that is a simple algebra and whose centre is exactly K.
- What is central simple algebra in Tamil?
- Central simple algebra in Tamil is மைய எளிய இயற்கணிதம். See Central simple algebra meaning in Tamil.
- How do you use central simple algebra in a sentence?
- This crossed product E#92;alphaG was introduced by Noether and played a significant role in the classical theory of central simple algebras.
- What part of speech is central simple algebra?
- Central simple algebra is a noun.
- What is the plural of central simple algebra?
- The plural of central simple algebra is central simple algebras.
Words near central simple algebra in the dictionary
Source and license
Adapted from Wiktionary: central simple algebra (page history and authors); central simple algebra (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “central simple algebra.” Word.ws, https://word.ws/central_simple_algebra. Based on Wiktionary, CC BY-SA 4.0.