Article contents
On Sands' questions concerning strong and hereditary radicals
Published online by Cambridge University Press: 18 May 2009
Extract
[7] Sands raised the following questions:
(1) Must a hereditary radical which is right strong be left strong?
(2) Must a right hereditary radical be left hereditary?
(3) (Example 6) Does there exist a right strong radical containing the prime radical β which is not left strong or hereditary?
Negative answers to questions (1) and (2) were given by Beidar [1].
In this paper we present different examples to answer (1) and (2), and we answer (3). We prove that the strongly prime radical defined in [4, 5] is right but not left strong. In the proof we use an example given by Parmenter, Passman and Stewart [6]. The same example and the strongly prime radical are used to answer (2) and (3).
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1986
References
REFERENCES
- 7
- Cited by