Article contents
A supernilpotent non-special radical class
Published online by Cambridge University Press: 17 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Let F be the upper radical determined by all fields. The supernilpotent radical classes which are not special have thus far always contained F properly. The purpose of this note is to construct a countably infinite number of supernilpotent radical classes which are not special and each of which is properly contained in F. The construction involves a ring due to Leavitt which is interesting in its own right and is not generally known. All rings considered are associative.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 9 , Issue 3 , December 1973 , pp. 343 - 348
- Copyright
- Copyright © Australian Mathematical Society 1973
References
[2]Рябухин, Ю.м. [Ju.M. Rjabuhin], О наднильпотентных и специальных радинах [On hypernilpotent and special radicals]. Issled. po algebre i matem. analizu, 65–72 (“Kartja Moldovenjaske”, Kisinev, 1965). Translated by WilliamG. Leavitt (unpublished).Google Scholar
[3]Snider, Robert L., “Lattices of radicals”, Pacific J. Math. 40 (1972), 207–220.CrossRefGoogle Scholar
- 10
- Cited by