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A Commutativity Condition for Rings

Published online by Cambridge University Press:  20 November 2018

Howard E. Bell
Howard E. Bell*
Affiliation:
Brock University, St. Catharines, Ontario
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The object of this paper is to prove the following theorem, a special case of which was previously explored in [1].

THEOREM. Let R be any associative ring with the property that

(†) for each x,y ∊ R, there exist integers m,n ≧ I for which xy = ymxn.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 986 - 991
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bell, H. E., Some commutativity results for rings with two-variable constraints, Proc. Amer. Math. Soc. 53 (1975), 280–284.Google Scholar
2. Corbas, B., Rings with few zero divisors, Math. Ann. 181 (1969), 1–7.Google Scholar
3. Corbas, B., Finite rings in which the product of any two zero divisors is zero, Arch. Math. 21 (1970), 466–469.Google Scholar
4. Faith, C., Algebraic division ring extensions, Proc. Amer. Math. Soc. 11 (1960), 43–53.Google Scholar
5. Herstein, I. N., Two remarks on the commutativity of rings, Canad. J. Math. 7 (1955), 411–412.Google Scholar
6. Herstein, I. N., On a result of Faith, Canadian Math. Bull. 18 (1975), 609.Google Scholar
7. Thierrin, G., On duo rings, Canadian Math. Bull. 3 (I960), 167–172.Google Scholar