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The Duals of the Camillo-Zelmanowitz Formulas for Goldie Dimension

Published online by Cambridge University Press:  20 November 2018

Joel K. Haack
Joel K. Haack*
Affiliation:
Department of MathematicsOklahoma State University, Stillwater, Ok 74078
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Abstract

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The duals of the Camillo-Zelmanowitz formulas for Goldie dimension are shown to hold for Varadarajan's notion of corank, subject to the existence of certain cocomplements. In particular, the formulas hold for modules over perfect rings. Also, if R is semiperfect, then the vector space dimension formulas hold for all modules over R for Goldie dimension iff they hold for corank iff R is semisimple.

Keywords

16A6416A5116A40CorankGoldie dimensionCamillo-Zelmanowitz formulasperfect ringsemisimple ring
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 325 - 334
Copyright
Copyright © Canadian Mathematical Society 1982

References

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