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A primitive ring which is a sum of two Wedderburn radical subrings
Author(s):
A.
V.
Kelarev
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2191-2193.
MSC (1991):
Primary 16N40;
Secondary 16N60
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Abstract:
We give an example of a primitive ring which is a sum of two Wedderburn radical subrings. This answers an open question and simplifies the proof of the known theorem that there exists a ring which is not nil but is a sum of two locally nilpotent subrings.
References:
- 1.
- M. Ferrero and E. R. Puczylowski, On rings which are sums of two subrings, Arch. Math. (1989), 4-10. MR 90f:16030
- 2.
- I. N. Herstein and L. W. Small, Nil rings satisfying certain chain conditions, Can. J. Math. 16 (1964), 771-776.
- 3.
- O. H. Kegel, Zur Nilpotenz gewisser assoziativer Ringe, Math. Ann. 149 (1963), 258-260. MR 28:3049
- 4.
- O. H. Kegel, On rings that are sums of two subrings, J. Algebra 1 (1964), 103-109. MR 29:3495
- 5.
- A. V. Kelarev, A sum of two locally nilpotent rings may be not nil, Arch. Math. 60 (1993), 431-435. MR 94c:16025
- 6.
- E. R. Puczylowski, Some questions concerning radicals of associative rings, ``Theory of Radicals'', Szekszárd, 1991, Coll. Math. Soc. János Bolyai 61(1993), 209-227. MR 94j:16033
- 7.
- A. Salwa, Rings that are sums of two locally nilpotent subrings, Comm. Algebra 24 (1996), 3921-3931. CMP 97:01
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Additional Information:
A.
V.
Kelarev
Affiliation:
Department of Mathematics, University of Tasmania, G.P.O. Box~252~C, Hobart, Tasmania~7001, Australia
Email:
kelarev@hilbert.maths.utas.edu.au
DOI:
10.1090/S0002-9939-97-04169-5
PII:
S 0002-9939(97)04169-5
Keywords:
Nilpotent rings,
locally nilpotent rings,
nil rings
Received by editor(s):
July 16, 1996
Additional Notes:
The author was supported by a grant of the Australian Research Council.
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1997,
American Mathematical Society
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