Encyclopedia > D > Dedekind domain
Dedekind domain
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is a Noetherian integral domain R whose localization RP at each maximal ideal P of R is a principal ideal domain; this entails RP is either a field or a discrete valuation ring. Alternatively, it can be defined as an integrally closed domain with Krull dimension at most 1.
Information are taken from Wikipedia, the open encyclopedia, to which contribute many volunteers from around the whole world. Texts are available under the following conditions GNU Free Documentation License.
Encyklopedie (cz) Encyklopédia (sk) Enzyklopädie (de)