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
