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An Answer to a Question of Kegel on Sums of Rings

Published online by Cambridge University Press:  20 November 2018

A. V. Kelarev
A. V. Kelarev*
Affiliation:
Department of Mathematics University of Tasmania G.P.O. Box 252 C Hobart, Tasmania 7001 Australia, e-mail: kelarev@hilbert.maths.utas.edu.au
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Abstract

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We construct a ring $R$ which is a sum of two subrings $A$ and $B$ such that the Levitzki radical of $R$ does not contain any of the hyperannihilators of $A$ and $B$. This answers an open question asked by Kegel in 1964.

Keywords

16N4016N60Nilpotent ringslocally nilpotent ringsnil rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 1 , 01 March 1998 , pp. 79 - 80
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Bahturin, Yu. and Kegel, O. H., Lie algebras which are universal sums of abelian subalgebras. Comm. Algebra 23 (1995), 2975–2990.Google Scholar
2. Beidar, K. I. and Mikhalev, A. V., Generalized polynomial identities and rings which are sums of two subrings. Algebra i Logika 34(1995) (1), 3–11.Google Scholar
3. Bokut’, L. A., Embeddings in simple associative algebras. Algebra i Logika 15 (1976), 117–142.Google Scholar
4. Ferrero, M. and Puczyłowski, E. R., On rings which are sums of two subrings. Arch. Math. 53 (1989), 4–10.Google Scholar
5. Herstein, I. N. and Small, L. W., Nil rings satisfying certain chain conditions. Canad. J. Math. 16 (1964), 771–776.Google Scholar
6. Kegel, O. H., Zur Nilpotenz gewisser assoziativer Ringe. Math. Ann. 149 (1963), 258–260.Google Scholar
7. Kegel, O. H., On rings that are sums of two subrings. J. Algebra 1 (1964), 103–109.Google Scholar
8. Kelarev, A. V., A sum of two locally nilpotent rings may be not nil. Arch.Math. 60 (1993), 431–435.Google Scholar
9. Kelarev, A. V., A primitive ring which is a sum of two Wedderburn radical subrings. Proc. Amer. Math. Soc., to appear.Google Scholar
10. Kepczyk, M. and Puczyłowski, E. R., On radicals of rings which are sums of two subrings. Arch.Math. 66 (1996), 8–12.Google Scholar
11. Puczyłowski, E. R., Some questions concerning radicals of associative rings. “Theory of Radicals”, Szekszárd, 1991, Coll. Math. Soc. János Bolyai 61 (1993), 209–227.Google Scholar
12. Salwa, A., Rings that are sums of two locally nilpotent subrings. Comm. Algebra 24 (1996), 3921–3931.Google Scholar