Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T11:05:29.582Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Britten, D. J., On Prime Jordan Rings H(R) with Chain Conditions, J. Algebra, 27 (1973), 414–421.CrossRefGoogle Scholar
2. Britten, D. J., On Semiprime Jordan Rings H(R) with ACQ, Proc. Amer. Math. Soc, 45 (1974), 175–178.Google Scholar
3. Erickson, T. S. and Montgomery, S., The Prime Radical in Special Jordan Rings, Trans. Amer. Math. Soc, 156 (1971), 155–164.CrossRefGoogle Scholar
4. Jacobson, N., Structure of Rings, 2nd ed., Amer. Math. Soc. Colloq. Publ., Vol. 37, Amer. Math. Soc., Providence, R.I., 1968.Google Scholar
5. Montgomery, Susan, Rings of Quotients for a Class of Special Jordan Rings, J. Algebra, 31 (1974), 154–165.CrossRefGoogle Scholar
6. Montgomery, Susan, Chain Condition on Symmetric Elements, Proc. Amer. Math. Soc. 46 (1974), 325–331.CrossRefGoogle Scholar