An archimedean group is a linearly ordered group which satisfies the Archimedean property, in which every positive element is bounded above by a natural number.
So an archimedean group has no infinite elements (and thus no non-zero infinitesimal elements).
Every archimedean group is an abelian group and has no bounded cyclic subgroups. Every archimedean group admits an embedding into the group of real numbers.
Every archimedean group is a flat module and a torsion-free group.
Every Dedekind complete archimedean group is isomorphic to the integers, if the group is not dense, or the Dedekind real numbers, if the group is dense.
Archimedean groups include
half integers?
Non-archimedean groups include
Last revised on January 9, 2023 at 00:51:14. See the history of this page for a list of all contributions to it.