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A Note on Quasi-Frobenius Rings and Ring Epimorphisms

Published online by Cambridge University Press:  20 November 2018

H. H. Storrer
H. H. Storrer*
Affiliation:
McGill University, Montreal
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In this note, we characterize quasi-Frobenius rings by a weakened form of the usual condition, that every ideal is an annihilator ideal.

We then apply this result to pure rings in the sense of Cohn and to dominant rings, a concept arising in the study of ring epimorphisms. All rings considered have a unit element.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 3 , June 1969 , pp. 287 - 292
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Bass, H., Finitistic dimension and a homological generalization of semi-primary rings. Trans. Amer. Math. Soc. 95 (1960) 466–488.Google Scholar
2. Cohn, P.M., On the free product of associative rings. Math. Z. 71 (1959) 380–398.Google Scholar
3. Dieudonné, J., Remarks on quasi-Frobenius rings. III. J. Math. 2 (1958) 346–354.Google Scholar
4. Isbell, J.R., Epimorphisms and dominions. Proc. of the Conference on Categorical Algebra. (Springer, Berlin, Heidelberg, New York 1966).Google Scholar
5. Levy, L. S., Commutative rings whose homomorphic images are self-injective. Pacific J. Math. 18 (1966) 149–153.Google Scholar
6. Nakayama, T., Supplementary remarks on Frobeniusean algebras I. Proc. Japan Acad. 25 (no. 7) (1949) 45–50.Google Scholar
7. Storrer, H. H., Epimorphismen von kommutativen Ringen, (to appear in Comm. Math. Helv.)Google Scholar
8. Wenger, R., Some semigroups having quasi-Frobenius algebras I. Proc. London Math. Soc. (3) 18 (1968) 484–494.Google Scholar