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The sum of two locally nilpotent rings may contain a free non-commutative subring
Author(s):
Anna
Fukshansky
Journal:
Proc. Amer. Math. Soc.
128
(2000),
383-386.
MSC (1991):
Primary 16N40;
Secondary 20M25
Posted:
July 6, 1999
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Abstract:
A family of examples of semigroup algebras is constructed each of which is a sum of two locally nilpotent subalgebras but yet contains a free subalgebra which is freely generated by two elements.
References:
- [1]
- O.H. Kegel, 'Zur Nilpotenz gewisser assoziativer Ringe', Math. Ann. 149(1962/63), 258-260. MR 28:3049
- [2]
- A.V. Kelarev, 'A sum of two locally nilpotent rings may be not nil', Arch. Math. 60(1993), 431-435. MR 94c:16025
- [3]
- A.V. Kelarev, 'A primitive ring which is a sum of two Wedderburn radical subrings', Proc. Amer. Math. Soc. 125 (1997), No.7, pp 2191-2193.MR 97i:16004
- [4]
- A. Salwa, 'Rings that are sums of two locally nilpotent subrings', Comm. Algebra 24(12)(1996), 3921-3931.MR 97e:16051
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Additional Information:
Anna
Fukshansky
Affiliation:
Martin-Luther-Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik, Institut für Algebra und Geometrie, 06099 Halle, Germany
Address at time of publication:
Department of Computer Science, Royal Holloway University of London, Egham Surrey TW20 0EX, United Kingdom
Email:
A.Fukshansky@dcs.rhbnc.ac.uk
DOI:
10.1090/S0002-9939-99-05005-4
PII:
S 0002-9939(99)05005-4
Keywords:
Nilpotent rings,
locally nilpotent rings,
nil rings
Received by editor(s):
October 9, 1997
Received by editor(s) in revised form:
April 9, 1998
Posted:
July 6, 1999
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1999,
American Mathematical Society
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