Wikipedia:Reference desk/Archives/Mathematics/2015 July 21

= July 21 =

Valuation ring with idempotent maximal ideal
Does there exist a valuation ring R, not a field, whose maximal ideal m is idempotent (m2 = m)? GeoffreyT2000 (talk) 02:27, 21 July 2015 (UTC)
 * Per one of the examples in the article "valuation ring", the ring of finite elements of the hyperreals is a valuation ring, and the ideal of infinitesimals is idempotent, as the infinitesimals are closed under square root. (It did make me think a little, though.  Thank you.)  — Arthur Rubin  (talk) 05:51, 21 July 2015 (UTC)
 * In fact, the finite elements of any non-Archimedean real-closed field will do, for the same reason. — Arthur Rubin  (talk) 06:01, 21 July 2015 (UTC)