[GAP Forum] ring theory

[Alexander Hulpke]

Dear Forum,

On Jan 21, 2011, at 10:23 PM, Igor Korepanov wrote:

> 
> gap> r := Ring( 10, 12 );
> <ring with 2 generators>
> gap> 10 in r;
> 
> - and GAP is still thinking over this very profound question.
> What did I miss?

The element test implemented fro rings in GAP first determines the element list of the ring and thus does not terminate for infinite rings. While I one could combine the element test in the computation of the element list and terminate once the element has been found, this still would be unsatisfactory in any example beyond trivial ones and not terminate if the element was not in the ring.

If there is a genuine need for element tests in infinite rings (beyond toy examples) I would be interested to know for what cases, since for situations such as polynomial rings alternatives might be possible.

Best,

   Alexander Hulpke