In
ring theory and related areas of
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
a central simple algebra (CSA) over a
field ''K'' is a finite-dimensional
associative ''K''-algebra ''A'' which is
simple
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*Simplicity, the state or quality of being simple
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* ''Simple'' (album), by Andy Yorke, 2008, and its title track
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* "Simple", a song by Johnn ...
, and for which the
center is exactly ''K''. (Note that ''not'' every simple algebra is a central simple algebra over its center: for instance, if ''K'' is a field of characteristic 0, then the
Weyl algebra