The sum of two locally nilpotent rings

may contain a free non-commutative subring

Author:
Anna Fukshansky

Journal:
Proc. Amer. Math. Soc. **128** (2000), 383-386

MSC (1991):
Primary 16N40; Secondary 20M25

DOI:
https://doi.org/10.1090/S0002-9939-99-05005-4

Published electronically:
July 6, 1999

MathSciNet review:
1622746

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Abstract | References | Similar Articles | Additional Information

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.

**[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:
https://doi.org/10.1090/S0002-9939-99-05005-4

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

Published electronically:
July 6, 1999

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 1999
American Mathematical Society