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Some Almost Simple Rings

Published online by Cambridge University Press:  20 November 2018

Paul Hill
Paul Hill*
Affiliation:
Florida State University, Tallahassee, Florida
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Herein, a ring is not required to have an identity. All rings are associative but not necessarily commutative. However, we specialize to the commutative case for some of our results. The paper is concerned primarily with rings having the property that all unbounded ideals or all unbounded homomorphic images are isomorphic to the ring. We say that a ring R is bounded if nR = 0 for some positive integer n; alternately, R, with or without 1, is said to have finite characteristic. Unbounded rings having the property that all proper subrings are bounded were characterized in [8].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 290 - 302
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Baer, R., Abelian groups without elements of finite order, Duke Math. J. 3 (1937), 68–122.Google Scholar
2. Chew, L. and Lawn, S., Residually finite rings, Can. J. Math. 22 (1970), 92–101.Google Scholar
3. Fried, E., On the subgroups of an abelian group that are ideals in every ring, Proceedings of the colloquium on abelian groups, Budapest, 1964.Google Scholar
4. Fuchs, L., Abelian groups (Hungarian Publishing House, Budapest, 1958).Google Scholar
5. Gilmer, R., Integral domains with noetherian subrings, Comment. Math.Helv. 45 (1970), 129–134.Google Scholar
6. Gilmer, R., Commutative rings in which each prime ideal is principal, Math. Ann. 183 (1969), 151–158.Google Scholar
7. Gilmer, R., Domains with integrally closed subrings, Math. Japon. 16 (1971), 9–11.Google Scholar
8. Gilmer, R., Lea, R., and M. O'Malley, Rings whose proper subrings have property P, Acta Sci. Math. (Szeged) 38 (1972), 69–75.Google Scholar
9. Gilmer, R. and O'Malley, M., Non-noetherian rings for which each proper subring is noetherian (preprint).Google Scholar
10. Herstein, I., Noncommutative rings (Math. Association of America, Carus monograph #15).Google Scholar
11. Levitz, K. and Mott, J., Rings with finite norm property, Can. J. Math. 24 (1972), 557–565.Google Scholar
12. Pierce, R., Homomorphisms of primary groups, in Topics in abelian groups (Scott, Foresman, Chicago, 1963).Google Scholar