The structure of left H-star algebras.
The basic results for finite dimensional algebras are due to Wedderburn [1]. Every finite dimensional algebra A which contains a non-zero nilpotent ideal has a non-zero radical R, and A/R is semi-simple (has a zero radical) and contains a unit element. Every semi-simple algebra is uniquely expressib...
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| Format: | Others |
| Language: | en |
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McGill University
1958
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| Online Access: | http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111441 |
| Summary: | The basic results for finite dimensional algebras are due to Wedderburn [1]. Every finite dimensional algebra A which contains a non-zero nilpotent ideal has a non-zero radical R, and A/R is semi-simple (has a zero radical) and contains a unit element. Every semi-simple algebra is uniquely expressible as a direct sum of a finite number of simple algebras, each with a unit element. In the infinite dimensional case the above structure theory still persists to some extent; that is, in certain cases a semisimple Banach algebra is a suitably generalized direct sum of suitably generalized matrix algebras. |
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