Archimedean ring
From Encyclopedia of Mathematics
A partially ordered ring the additive group of which is an Archimedean group with respect to the given order. An Archimedean totally ordered ring 
is either a ring with zero multiplication (i.e. 
for all 
and 
in 
) over an additive group which is isomorphic to some subgroup of the group of real numbers, or else is isomorphic to a unique subring of the field of real numbers, taken with the usual order. An Archimedean totally ordered ring is always associative and commutative.
References
| [1] | L. Fuchs, "Partially ordered algebraic systems" , Pergamon (1963) |
How to Cite This Entry:
Archimedean ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Archimedean_ring&oldid=31540
Archimedean ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Archimedean_ring&oldid=31540
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article