central simple algebra
短语词形变化
central simple algebras
复数
central simple algebras
别名
CSA
释义与例句
n.
-
1.
A finite-dimensional associative algebra over some field K that is a simple algebra and whose centre is exactly K.
数学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).