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On Semiprime Ample Jordan Rings

J ⊆ H with Chain Condition

Published online by Cambridge University Press:  20 November 2018

Daniel J. Britten
Daniel J. Britten*
Affiliation:
Department of Mathematics, University of Windsor, Windsor, Ontario, Canada
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The purpose of this paper is to point out that the arguments of [2] with slight modification extend the main result of [2] to the case of H satisfying either ACC or DCC on quadratic ideals and they extend [6, Theorem 2] to R being semiprime. Thus we obtain

Theorem 1. Let R be a semiprime associative ring with involution ✶ and J a closed ample quadratic Jordan subring of H(R) satisfying either ACC or DCC on quadratic ideals. Then R is Goldie. In this case, J has a Jordan ring of quotients J′ which is a closed ample quadratic Jordan subring of H(R′) where R′ is the associative ring of quotients of R.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 145 - 148
Copyright
Copyright © Canadian Mathematical Society 1976

Footnotes

(1)

Prepared while the author was at the 1974 SRI at the University of Calgary and held NRC Grant A-8471. Revised while the author was at the 1975 SRI at Dalhousie University.

References

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3. Erickson, T. S. and Montgomery, S., The Prime Radical in Special Jordan Rings, Trans. Amer. Math. Soc, 156 (1971), 155–164.CrossRefGoogle Scholar
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