Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T19:43:50.188Z Has data issue: false hasContentIssue false

On questions of B. J. Gardner and A. D. Sands

Published online by Cambridge University Press:  09 April 2009

K. I. Beidar
Affiliation:
Department of Algebra, Moscow State University, 117234 Moscow, USSR
Rights & Permissions [Opens in a new window]

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.

An example of two disjoint special classes whose upper radicals coincide is presented. It is shown that the left hereditary subradical of the hereditary idempotent radical is right hereditary. An example of a hereditary and principally left hereditary radical which is not left hereditary is constructed.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Anderson, T., Divinsky, N. and Sulinski, A., ‘Hereditary radicals in associative and alternative rings’, Canad. J. Math. 17 (1965), 594603.Google Scholar
[2]Andrunakievich, V. A. and Ryabukhin, Ju. M., Radicals in algebras and structural theory (Nauka, Moscow, 1979) (in Russian).Google Scholar
[3]Beidar, K. I., ‘Atoms in the lattice of radicals’, Mat. Issled. 85 (1985), 2131 (in Russian).Google Scholar
[4]Divinsky, N., Rings and radicals (Allen and Unwin, London, 1965).Google Scholar
[5]Forsythe, A. and McCoy, N. H., ‘On the commutativity of certain rings’, Bull. Amer. Math. Soc. 52 (1946), 523526.Google Scholar
[6]Gardner, B. J. (ed.), Rings, modules and radicals, (Proceedings of the Hobart Conference, 1987), Research Notes in Mathematics 204 (Pitman, London, 1989).Google Scholar
[7]Goodearl, K. R., Von Neumann regular rings (Pitman, London, 1979).Google Scholar
[8]Heyman, G. A. P. and Roos, C., ‘Essential extension in radical theory of rings’, J. Austral. Math. Soc. (Series A) 23 (1977), 340347.CrossRefGoogle Scholar
[9]Sands, A. D., ‘Radical properties and one sided ideals’, in: Contribution to general algebra 4, Proceedings of the Krems Conferences 1985 (Hölder-Pichler-Temsky, Vienna, 1987) pp. 151171.Google Scholar
[10]Szász, F. A., Radicals of rings (Akadémiai Kiado, Budapest, 1981).Google Scholar
[11]Wiegandt, R., Radical and semisimple classes of rings, Queen's papers in pure and applied mathematics 37 (Kingston, Ontario, 1974).Google Scholar