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H-extension of ring

Published online by Cambridge University Press:  09 April 2009

Bertrand I-Peng Lin
Bertrand I-Peng Lin
Affiliation:
National Taiwan University
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A ring R is called an H-ring if for every x ∈ R there exists an interger n=n(x)> 1 such that xn-x ∈C, where C is center of R. I. N. Herstein proved that H-rings must be commutative [See 3 pp. 220–221]. We now introduce the following definition.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 236 - 240
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Armendariz, E. P., ‘On Radical Extension of Ratings’, J. Australian Math. Soc. 7, (1967), 552–554.CrossRefGoogle Scholar
[2]Faith, C., ‘Algebraic Division Ring Extension’, Proc. Amer. Math. Soc. 11, (1960), 43–43.CrossRefGoogle Scholar
[3]Jacobson, N., ‘Structure of Rings’, (Amer. Math. Soc. 1956).CrossRefGoogle Scholar
[4]Martindale III, W. S., ‘The Commutativity of a Special Class of Rings’, Canadian J. Math. 12, (1960), 263–268.CrossRefGoogle Scholar