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.
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Joel K. Haack (1982) studied this question.
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