It is well known that if A is a
compact integral domain and R is its Jacobson radical, then A = R or A∕R is a
division ring and A has an identity. The object of this paper is to investigate some of
the algebraic properties of A. If A has an identity and finite characteristic,
then there exists a maximal subfield F of A which is isomorphic to A∕R.
Furthermore A is topologically isomorphic to F + R. The existence of a subfield
is a necessary and sufficient condition for A to have finite characteristic.
If A does not have an identity bul does have finite characteristic, then it
can be openly embedded in a compact integral domain with an identity.
Finally, the main result shows that if the center of A is open, then A is
commutative.
