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. 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).