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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

1. Anderson, F. W. and Fuller, K. R., Rings and Categories of Modules, Springer-Verlag, New York, 1973.Google Scholar
2. Camillo, V. P., On a conjecture of Herstein, J. Algebra 50 (1978), 274-275.Google Scholar
3. Camillo, V. P. and Zelmanowitz, J., On the dimension of a sum of modules, Comm. Algebra 6 (1978), 353-360.Google Scholar
4. Fleury, P., A note on dualizing Goldie dimension, Canad. Math. Bull. 17 (1974), 511-517.Google Scholar
5. Kasch, F. R. and Mares, E. A., Eine Kennzeichnung semiperfecter Moduln, Nagoy. Math. J. 27 (1966), 525-529.Google Scholar
6. Reiter, E. E., Thesis, University of Cincinnati, 1978.Google Scholar
7. Sarath, B. and Varadarajan, K., Dual Goldie dimension-II, Comm. Algebra 7 (1979), 1885-1889.Google Scholar
8. Varadarajan, K., Dual Goldie dimension, Comm. Algebra 7 (1979) 565-610.Google Scholar
9. Varadarjan, K., Modules with supplements, Pacifi. J. Math. 82 (1979), 559-564.Google Scholar