And if the polynomial ring is in finitely many variables, you at least stand a chance, and the reference I quoted is irrelevant, EXCEPT to show that you do need to use this knowledge about the field,
On Wednesday, 18 April 2012 20:50:26 UTC+1, diophan wrote: > > I'll check out the reference. If it makes the situation any better the > ring is a quotient of a polynomial ring over a finite field. > > On Wednesday, April 18, 2012 3:03:45 PM UTC-4, JamesHDavenport wrote: >> >> I would doubt it very much. I imagine the same techniques >> as Fr\"ohlich,A. & Shepherdson,J.C., Effective Procedures in Field >> Theory. Phil, Trans. Roy. Soc. Ser. A 248(1955-6) pp. 407-432, can be used >> to construct a ring which has nontrivial idempotents iss we can determine >> membership in a recursively enumerable sequence. I think you would need to >> know how the ring was constructed. >> >> On Tuesday, 17 April 2012 19:37:29 UTC+1, diophan wrote: >>> >>> Is there any way in sage to determine if a commutative ring with unity R >>> has any idempotents other than 0 or 1? My R's have infinitely many elements >>> so squaring all the elements isn't going to work. This is equivalent to R >>> being isomorphic to a product of two non-trivial rings. >>> >>> -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
