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Coranks of a quasi-projective module and its endomorphism ring

Published online by Cambridge University Press:  18 May 2009

Tsutomu Takeuchi
Tsutomu Takeuchi
Affiliation:
Department of Mathematics, Faculty of Education, Hirosaki University, Hirosaki, 036, Japan
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Recently several authors have studied dualizing Goldie dimension of a module: spanning dimension in [2], codimension in [13], corank in [16] and also [9,17,12, 5,11, 6, 4, 7] ([13] may be read in comparison with the others). In the present note we prove the equality corank RP = corank SS, where P is a quasi-projective left R-module and S is its endomorphism ring. This result is an answer to the question [12, p. 1898] and an extension of [3, Corollary 4.3] which shows the above equality for a Σ-quasi-projective left R-module P.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 381 - 383
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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