Prime rings with involution whose symmetric zero-divisors are nilpotent
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- by P. M. Cohn PDF
- Proc. Amer. Math. Soc. 40 (1973), 91-92 Request permission
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).References
- P. M. Cohn, Free rings and their relations, London Mathematical Society Monographs, No. 2, Academic Press, London-New York, 1971. MR 0371938
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 91-92
- MSC: Primary 16A12; Secondary 16A28
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318202-5
- MathSciNet review: 0318202