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On Prime Rings with Ascending Chain Condition on Annihilator Right Ideals and Nonzero Infective Right Ideals

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh  and
A. C. Mewborn
Kwangil Koh
Affiliation:
North Carolina State University, Raleigh, North Carolina
A. C. Mewborn
Affiliation:
University of North Carolina, Chapel Hill, North Carolina
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If I is a right ideal of a ring R, I is said to be an annihilator right ideal provided that there is a subset S in R such that

I is said to be injective if it is injective as a submodule of the right regular R-module RR. The purpose of this note is to prove that a prime ring R (not necessarily with 1) which satisfies the ascending chain condition on annihilator right ideals is a simple ring with descending chain condition on one sided ideals if R contains a nonzero right ideal which is injective.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 443 - 444
Copyright
Copyright © Canadian Mathematical Society 1971

References

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