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Re: [Axiom-developer] Question concerning types...

From: Bertfried Fauser
Subject: Re: [Axiom-developer] Question concerning types...
Date: Mon, 18 Sep 2006 14:31:15 +0200 (CEST)

On Mon, 18 Sep 2006, Ralf Hemmecke wrote:


a very interesting discussion! Perhaps you might enjoy reading 'The
Skeleton Key' by Dudley E. Littlewood, where the nature of indeterminates
is nicely contemplated.

>From my point of view, could you please explain, why an indeterminate
should behave like the original ring it was abstracted from. This is
uncategorical. Furthermore, there are many ionstances of problems where
inderterminates need to be specified or extendedly specified to make sense
at all or to solve a problem oin a meaningful way, eg Galois theory.

Would you agree that one should try to have say a Ring (integers) and
another algebraic structure (indeterminates) which might have several
attirbutes (associative, power associative, alternative, commutative,
ring, group,....) and that one builds up a new algebra from the
(semi/direct) product of the two algebraic structures at hand.

The diagram in a previous mail wants to define a sort of functor, but then
one has to specify the target category cxarefully! I do not beliefe that
there is such a generalization, usually one has to put severe restrictions
of tyhe nature and number of indeterminates to be able to construct
meaningfull algebraic objects.

Please go ahead with your refreshing discussion...


% PD Dr Bertfried Fauser
%     Institution: Max Planck Institute for Math, Leipzig 
%   Privat Docent: University of Konstanz, Phys Dept 
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%          Phone : Leipzig +49 341 9959 735  Konstanz +49 7531 693491

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