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Notes on weakly-semisimple rings

Published online by Cambridge University Press:  17 April 2009

Yiqiang Zhou
Yiqiang Zhou
Affiliation:
Department of MathematicsUniversity of British ColumbiaVancouver BCV6T 1Z2Canada.
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Abstract

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Responding to a question on right weakly semisimple rings due to Jain, Lopez-Permouth and Singh, we report the existence of a non-right-Noetherian ring R for which every uniform cyclic right it-module is weakly-injective and every uniform finitely generated right R-module is compressible. We show that a ring R is a right Noetherian ring for which every cyclic right R-module is weakly R-injective if and only if R is a right Noetherian ring for which every uniform cyclic right R-module is compressible if and only if every cyclic right R-module is compressible. Finally, we characterise those modules M for which every finitely generated (respectively, cyclic) module in σ[M] is compressible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 3 , December 1995 , pp. 517 - 525
Copyright
Copyright © Australian Mathematical Society 1995

References

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