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Factor-Correspondences in Regular Rings

Published online by Cambridge University Press:  20 November 2018

S. K. Berberian
S. K. Berberian*
Affiliation:
The University of Texas at Austin, Austin, Texas
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Factor-correspondences are nothing more than a way of describing isomorphisms between principal ideals in a regular ring. However, due to a remarkable decomposition theorem of M. J. Wonenburger [7, Lemma 1], they have proved to be a highly effective tool in the study of completeness properties in matrix rings over regular rings [7, Theorem 1]. Factor-correspondences also figure in the proof of D. Handelman's theorem that an ℵ0-continuous regular ring is unitregular [4, Theorem 3.2].

The aim of the present article is to sharpen the main result in [7] and to re-examine its applications to matrix rings. The basic properties of factor-correspondences are reviewed briefly for the reader's convenience.

Throughout, R denotes a regular ring (with unity).

Definition 1 (cf. [5, p. 209ff], [7, p. 212]). A right factor-correspondence in R is a right R-isomorphism φ : J → K, where J and K are principal right ideals of R (left factor-correspondences are defined dually).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 1 , 01 February 1982 , pp. 23 - 30
Copyright
Copyright © Canadian Mathematical Society 1982

References

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