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Weakly prime one-sided ideals

Published online by Cambridge University Press:  09 April 2009

Andries P. J. Van Der Walt
Andries P. J. Van Der Walt
Affiliation:
Department of Mathematics University of StellenboschStellenbosch, Republic of South Africa
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Abstract

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A left ideal P in a ring is weakly prime if L, K ⊇ P and LK ⊆ P for left ideals L and K imply L = P or K = P. A prime left ideal is weakly prime but the converse is false. Characterizations of weakly prime left ideals as well as a number of their properties are obtained. The intersection of all the weakly prime left ideals in a ring is a left ideal which in general is contained in (but not equal to) the prime radical.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 1 , February 1985 , pp. 84 - 91
Copyright
Copyright © Australian Mathematical Society 1985

References

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