Vol. 32, No. 3, 1970

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Compact integral domains

Joe Ebeling Cude

Vol. 32 (1970), No. 3, 615–619

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.

Mathematical Subject Classification
Primary: 16.98
Received: 5 June 1969
Published: 1 March 1970
Joe Ebeling Cude