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On a Condition of J. Ohm for Integral Domains1

Published online by Cambridge University Press:  20 November 2018

Robert Gilmer
Robert Gilmer*
Affiliation:
Florida State University, Tallahassee, Florida
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This paper originated mainly from results presented in a paper by J. Ohm (13), and, to a lesser degree, from results of Gilmer in (3). Ohm's paper is concerned with the validity of the equation (x, y)n = (xn, yn) for each pair of elements x, y of an integral domain D with identity. If D is a Prüfer domain, the above equation is valid for all x, y ϵ D (7, p. 244). Butts and Smith have shown (2) that if (x, y)2 = (x2, y2) for all x, y of the integrally closed domain D, then D is a Priifer domain.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 970 - 983
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

1.

The author was supported during the writing of this paper by Alfred P. Sloan Foundation.

References

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