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Rings All of whose Factor Rings are Semi-Prime

Published online by Cambridge University Press:  20 November 2018

R.C. Courter
R.C. Courter*
Affiliation:
Wayne State University, Detroit, Michigan 48202
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We prove in this paper that fifteen classes of rings coincide with the class of rings named in the title. One of them is the class of rings R such that X2 = X for each R-ideal X: we shall refer to rings with this property (and thus to the rings of the title) as fully idempotent rings. The simple rings and the (von Neumann) regular rings are fully idempotent. Indeed, every finitely generated right or left ideal of a regular ring is generated by an idempotent [l, p. 42], so that X2 = X holds for every one-sided ideal X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 417 - 426
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Faith, C., Lectures on Injective Modules and Quotient Rings. (New York, Springer-Verlag, 1967).Google Scholar
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3. Sasiada, E., Solution of the problem of existence of a simple radical ring. Bull. Acad. Polon. Sci. 9 (1961) 257.Google Scholar