Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference7 articles.
1. Lower, Radical Properties for Associative and Alternative Rings;Anderson;J. London Math. Soc.,1966
2. [7] Yu-Lee Lee , ‘On Intersections and Unions of Radical Classes’, J. Aust. Math. Soc. (To appear).
3. Radicals in Rings and Algebras;Kurosh;Math. Sb.,1953
4. The Hereditary Property in the Lower Radical Construction
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献