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A Note on a Prime Ring with a Maximal Annihilator Right Ideal

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh
Kwangil Koh*
Affiliation:
North Carolina State of the University of North Carolina at Raleigh
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A ring R is called a prime ring [1] if and only if a·R·b = 0 implies that a = 0 or b = 0 for all a, b ϵ R. Hence if R is a prime ring and a is a non-zero element of R, a·R ≠ 0 and R·a ≠ 0. In the present note we prove that a prime ring with a maximal annihilator right ideal has no non-zero nil right or left ideal.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 1 , February 1965 , pp. 109 - 110
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. McCoy, N.H., Prime ideals in general rings, Amer. J. Math., vol. 71(1949), pp. 823-833.Google Scholar