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Direct-sum decomposition of atomic and orthogonally complete rings

Published online by Cambridge University Press:  09 April 2009

Alexander Abian
Alexander Abian
Affiliation:
Iowa State University Ames, Iowa
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In this paper we give a necessary and sufficient condition for decomposition (as a direct sum of fields) of a ring R in which for every x ∈ R there exists a (and hence the smallest) natural number n(x) > 1 such that . We would like to emphasize that in what follows R stands for a ring every element x of which satisfies (1).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 357 - 361
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Jacobson, N., Structure of Rings, Amer. Math. Soc. Coll. Publ. Vol. 37 (1956), p. 217.Google Scholar