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On Continuous Regular Rings

Published online by Cambridge University Press:  20 November 2018

Y. Utumi
Y. Utumi*
Affiliation:
Osaka Women' s University and McGill University
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A subset K of a lattice is said to be directed if for any a, b∊K there is c∊K with c ≥ a, b. A complete lattice L is called upper continuous if for every directed subset (aα) and every element b.

The following is a slight improvement of [4; Anmerkung 1. 11, p. 11].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 1 , January 1961 , pp. 63 - 69
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Johnson, R. E., The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891-895.Google Scholar
2. Levitzki, J., Structure of algebraic algebras and related rings, Trans. Amer. Math. Soc. 74 (1953), 384-409.Google Scholar
3. Levitzki, J., Some theorems concerning associative Zorn rings, Bull. Res. Council Israel 3 (1954), 380-384.Google Scholar
4. Maeda, F., Kontinuierliche Geometrien (Springer, 1958).Google Scholar
5. Utumi, Y., On quotient rings, Osaka Math. J. 8 (1956), 1–18.Google Scholar
6. Utumi, Y., On a theorem on modular lattices, Proc . Japan Acad. 35(1959), 16–21.Google Scholar
7. Utumi, Y., On continuous regular rings and semi-simple self injective rings, Canad. J. Math. 12 (1960), 597–605. Google Scholar