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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Prime rings with involution whose symmetric zero-divisors are nilpotent


Author: P. M. Cohn
Journal: Proc. Amer. Math. Soc. 40 (1973), 91-92
MSC: Primary 16A12; Secondary 16A28
MathSciNet review: 0318202
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Abstract: Let $ k$ be a field and $ R$ the $ k$-algebra generated by $ x$ and $ y$ with the single defining relation $ {x^2} = 0$. Using free ring techniques we prove that the set of left zero-divisors of $ R$ is $ Rx$. There is a unique involution fixing $ x,y$ and this makes $ R$ into a prime ring with involution whose symmetric zero-divisors are nilpotent (answering a question by W. S. Martindale). This example also provides us with a subfunctor of the identity whose value is a onesided ideal (answering a question by R. Baer).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0318202-5
PII: S 0002-9939(1973)0318202-5
Keywords: Prime ring, involution, zero-divisor, nilpotent, free ring, weak algorithm
Article copyright: © Copyright 1973 American Mathematical Society