On Mon, 18 Sep 2006, Ralf Hemmecke wrote: Hi,
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... ciao BF. % PD Dr Bertfried Fauser % Institution: Max Planck Institute for Math, Leipzig <http://www.mis.mpg.de> % Privat Docent: University of Konstanz, Phys Dept <http://www.uni-konstanz.de> % contact|->URL : http://clifford.physik.uni-konstanz.de/~fauser/ % Phone : Leipzig +49 341 9959 735 Konstanz +49 7531 693491 _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer