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A Non-Trivial Ring with Non-Rational Injective Hull

Published online by Cambridge University Press:  20 November 2018

P. Berthiaume
P. Berthiaume*
Affiliation:
Rutgers - The State University
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Several authors have investigated "rings of quotients" of a given ring R . (See, for example, Johnson [7], Johnson and Wong [8], Utumi [11], Findlay and Lambek [5], Lambek [9], and Bourbaki [2].)

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967 , pp. 275 - 282
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Baer, R., Abelian groups that are direct summands of every containing Abelian group. Bull. Amer. Math. Soc. 46 (1944), p. 800-806.Google Scholar
2. Bourbaki, N., Elèments de Mathèmatique. Vol. 29, Paris (1966).Google Scholar
3. Cartan, H. and Eilenberg, S., Homological Algebra. Princeton University Press (1955).Google Scholar
4. Eckmann, B. and Schopf, A., Überinjektive Moduln. Arch. Math. 4 (1955), pages 75-78.Google Scholar
5. Findlay, G. D. and Lambek, J., A generalized ring of quotients. Can. Math. Bull. 1 (1955), pages 77-85, 155-167.Google Scholar
6. Johnson, R. E., The extended centralizer of a ring over a module. Proc. Amer. Math. Soc. 2 (1955), pages 891-895.Google Scholar
7. Johnson, R. E., Quotient rings of rings with zero singular ideal. Pacific J. Math. 11 (1966), pages 1385-1395.Google Scholar
8. Johnson, R. E. and Wong, E. T., Self-injective rings. Can. Math. Bull. 2 (1955), pages 167-174.Google Scholar
9. Lambek, J., On Utumi′s ring of quotients. Can. J.Math. 15 (1966), pages 363-370.Google Scholar
10. Osofsky, B. L., On ring properties of injective hulls. Can. Math. Bull. 7 (1966), pages 405-413.Google Scholar
11. Utumi, Y., On quotient rings. Osaka Math. J. 8 (1955), pages 1-18.Google Scholar
12. Utumi, Y., On a theorem on modular lattices. Proc. Japa. Acad. 35 (1955), pages 16-21.Google Scholar