Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T14:13:20.677Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower radicals in nonassociative rings

Published online by Cambridge University Press:  09 April 2009

R. Tangeman  and
D. Kreiling
R. Tangeman
Affiliation:
University of Florida Western Illinois UniversityMacomb, Illinois 61455 U.S.A.
D. Kreiling
Affiliation:
University of Florida Western Illinois UniversityMacomb, Illinois 61455 U.S.A.
Rights & Permissions [Opens in a new window]

Extract

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 W be a universal class of (not necessarily associative) rings and let A ⊆ W. Kurosh has given in [6] a construction for LA, the lower radical class determined by A in W. Using this construction, Leavitt and Hoffmann have proved in [4] that if A is a hereditary class (if K ∈ A and I is an ideal of K, then I ∈ A), then LA is also hereditary. In this paper an alternate lower radical construction is given. As applications, a simple proof is given of the theorem of Leavitt and Hoffmann and a result of Yu-Lee Lee for alternative rings is extended to not necessarily associative rings.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 4 , December 1972 , pp. 419 - 423
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Anderson, T., Divinsky, N. and Sulinsky, A., ‘Lower, Radical Properties for Associative and Alternative Rings’; J. London Math. Soc. 41 (1966), 417–424.Google Scholar
[2]Amitsur, S. A., ‘Radicals in Rings and Bicategories’, Amer. J. Math. 76 (1954), 100–125.CrossRefGoogle Scholar
[3]Armendariz, E. P. and Leavitt, W. G., ‘The Hereditary Property in the Lower Radical Construction’, Canad. J. Math. 20 (1968), 474–476.CrossRefGoogle Scholar
[4]Hoffman, A. E. and Leavitt, W. G., ‘Properties Inherited by the Lower Radical.’ Protugaliae Mathematica 27 (1968), 63–66.Google Scholar
[5]Jacobson, N., Structure of Rings (Amer. Math. Soc. Coll. Publ. 37, Providence, 1956).Google Scholar
[6]Kurosh, A., ‘Radicals in Rings and Algebras’, Math. Sb. 33, (1953), 13–26.Google Scholar
[7]Yu-Lee, Lee, ‘On Intersections and Unions of Radical Classes’, J. Aust. Math. Soc. (To appear).Google Scholar