Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-rn2sj Total loading time: 0.383 Render date: 2022-08-17T12:41:59.169Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Semisimplicity of Free Centred Extensions

Published online by Cambridge University Press:  20 November 2018

Miguel Ferrero*
Affiliation:
Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900 Porto Alegre Brazil, e-mail:Ferrero@ifI.ufrgs.br
Rights & Permissions[Opens in a new window]

Abstract

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

We prove that a free centred extension R[E] is a semisimple ring if R is a semisimple ring and C[E] is semisimple for every field C which is the extended centroid of a primitive factor of R.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Ferrero, M., Closed and prime ideals in free centred extensions, J. Algebra 148(1992), 116.Google Scholar
2. Ferrero, M., Centred bimodules over prime rings: closed submodules and applications to ring extensions, J. Algebra, to appear.Google Scholar
3. Ferrero, M. and Parmenter, M. M., A note on Jacobson rings and polynomial rings, Proc. Amer. Math. Soc. 104(1988), 281286.Google Scholar
4. Krempa, J., On semisimplicity of tensor products, Lecture Notes in Pure and Appl. Math. 51, Dekker, New York, 1979, 105122,Google Scholar
5. Passman, D. S., The algebraic structure of group rings, John Wiley, New York, 1977.Google Scholar
6. Stenström, B., Rings of quotients, Springer-Verlag, Berlin, Heidelberg, New York, 1975.CrossRefGoogle Scholar
You have Access
2
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Semisimplicity of Free Centred Extensions
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Semisimplicity of Free Centred Extensions
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Semisimplicity of Free Centred Extensions
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *