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On balanced one-sided ideals

Published online by Cambridge University Press:  17 April 2009

T. G. Schultz
T. G. Schultz
Affiliation:
Mathematics Dept, University of the Western Cape, Bellville 7530, Republic of South Africa.
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Abstract

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The relation between the subclass X of balanced one-sided ideals, which contains all two-sided ideals, and weakly prime one-sided ideals is considered. If a member P of X is prime, then it is prime in its idealizer I (P). Furthermore, if the ring is left and right noetherain, then I (P) modulo P is a prime Goldie ring.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 1 , August 1986 , pp. 79 - 86
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Fitting, H., “Primarkomponentenzerlegung in nichtkommutativen Ringen”, Math. Ann. 11 (1935), 19–41.CrossRefGoogle Scholar
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[3]Van Der Walt, A. P. J., “Weakly prime one-sided ideals”, J. Australian Math. Soc. Ser. A, 38 (1985), 84–91.CrossRefGoogle Scholar