Talk:Semisimple algebra

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[edit] Algebra associative?

I assume that here in this context an algebra is meant to be associative, right? (AFAIK ideals in non-associative algebras don't make much sense.) Since it's not universally agreed upon whether an algebra should be associative or non-associative (e.g. the article Algebra (ring theory) takes all algebras to be associative while the article Algebra over a field assume them to be non-associative by default) , I think it would be wise to explicitly say so. (ezander) 134.169.77.186 14:56, 7 May 2007 (UTC)

[edit] Finite dimensional? Jacobson radical

From Dales "Banach algebras and Automatic continuity" I have the definition of "semisimple" for a algebra to be that the Jacobson radical is zero. Is this equivalent to definition here in the finite dimensional case, or do we have different things with the same nameA Geek Tragedy 20:54, 25 May 2007 (UTC)?

OK I should read more carefully. It IS the same! In which case can we have the characterisation using the radical as the defintion (in the general case) and the current definition as "Theorem: If A is finite dimensional this is the same as..."? The general version is needed in some functional analysis settings.A Geek Tragedy 20:59, 25 May 2007 (UTC)