Geodesic
Factor-Correspondences in Regular Rings
Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 23-30

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Berberian, S. K. Factor-Correspondences in Regular Rings. Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 23-30. doi: 10.4153/CJM-1982-004-0
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