An archimedean integral domain is an ordered integral domain that satisfies the archimedean property.
Every archimedean integral domain extension of the integers is a dense linear order.
Since is archimedean, it does not have either infinite or infinitesimal elements, which means there exists an integer and natural number such that and . implies and for all and in . Let . Since there exists an element such that for all and , is a dense linear order.
This means that the Dedekind completion of every archimedean integral domain extension of the integers is the integral domain of real numbers.
Archimedean integral domains include
Non-archimedean integral domains include
Last revised on May 30, 2022 at 10:57:37. See the history of this page for a list of all contributions to it.