Difference between revisions of "Simple algebra"
From Encyclopedia of Mathematics
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| − | An algebra, consisting of more than one element, without two-sided ideals different from | + | {{TEX|done}} |
| + | An algebra, consisting of more than one element, without two-sided ideals different from $0$ and the entire algebra. A simple algebra without a unit element need not be a [[simple ring]], since in this case not every ideal in the ring is an ideal in the algebra. The classification of the finite-dimensional simple algebras is known for certain classes of algebras (cf. [[Alternative rings and algebras]]; [[Jordan algebra]]; [[Lie algebra]]). Every associative algebra over a field possessing a unit element is imbeddable in a simple algebra with the same unit element. | ||
| − | For references, see [[ | + | For references, see [[Simple ring]]. |
Latest revision as of 20:33, 28 December 2014
An algebra, consisting of more than one element, without two-sided ideals different from $0$ and the entire algebra. A simple algebra without a unit element need not be a simple ring, since in this case not every ideal in the ring is an ideal in the algebra. The classification of the finite-dimensional simple algebras is known for certain classes of algebras (cf. Alternative rings and algebras; Jordan algebra; Lie algebra). Every associative algebra over a field possessing a unit element is imbeddable in a simple algebra with the same unit element.
For references, see Simple ring.
How to Cite This Entry:
Simple algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_algebra&oldid=13990
Simple algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_algebra&oldid=13990
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article