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On Duo Rings

Published online by Cambridge University Press:  20 November 2018

G. Thierrin
G. Thierrin*
Affiliation:
University of Montreal and Summer Research Institute, Kingston
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Following E. H. Feller [l], a ring R is called a duo ring if every one-sided ideal of R is a two-sided ideal.

In the first part of this paper, we give some properties of duo rings and we show that the set of the nilpotent elements of a duo ring R is an ideal, the intersection of the completely prime ideals of R.

It is easy to see that every duo ring is a subdirect sum of subdirectly irreducible duo rings. We give in the second part of this paper a characterization of the subdirectly irreducible duo rings. This characterization is quite similar to the characterization of the subdirectly irreducible commutative rings, due to N. H. McCoy [2], whose methods we use.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 2 , 01 May 1960 , pp. 167 - 172
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Feller, E. H., Properties of primary noneommutative rings, Trans. Amer. Math. Soc. 89 (1958), 79-91.Google Scholar
2. McCoy, N. H., Subdirectly irreducible commutative rings, Duke Math. J. 12 (1945), 381-387.Google Scholar
3. McCoy, N. H., Prime ideals in general rings, Amer. J. Math. 71 (1949), 823-833.10.2307/2372366Google Scholar