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Self-Injective Rings

Published online by Cambridge University Press:  20 November 2018

E.T. Wong  and
R.E. Johnson
E.T. Wong
Affiliation:
Oberlin College, U.S.A.
R.E. Johnson
Affiliation:
Smith College, U.S.A.
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Historically, the first example of a ring of quotients was the quotient field of an integral domain. Later on, conditions were found under which a noncommutative integral domain has a quotient division ring. More recently, R.E. Johnson [4], Y. Utumi [5], and G.D. Findlay and J. Lambek [3] have discussed the existence and structure of a maximal ring of quotients of any ring.

The present paper uses the methods of Findlay and Lambek to recast the results of Johnson on the quotient ring of a ring with zero singular ideal. It is also shown that such a ring has a unique left-right maximal ring of quotients.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 3 , 01 September 1959 , pp. 167 - 173
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Eckmann, B. and Schopf, A., ?ber injektive Moduln, Archiv derMath. 4 (1953), 75-78.Google Scholar
2. Cartan, H. and Eilenberg, S, Homological algebra, (Princeton, 1956).Google Scholar
3. Findlay, G.D. and Lambek, J., A generalized ring of quotients I, H, Can. Math. Bull. 1 (1958), 77-85, 155-167.Google Scholar
4. Johnson, R.E., The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891-895.Google Scholar
5. Johnson, R.E., Structure theory of faithful rings II, Trans. Amer. Math. Soc. 84 (1957), 523-542.Google Scholar
6. Utumi, Y., On quotient rings, Osaka Math. J. 8 (1956), 1-18.Google Scholar
7. von Neumann, J., On regular rings, Proc. Nat. Acad. Sci. U.S.A. 22 (1936), 707-713.Google Scholar