Abstract
In this paper, we give a new proof of the n factorial theorem of Suslin on unimodular rows. The theorem of Suslin is proved by looking at the one cocycle associated with the projective module given by the unimodular row and proving that the cocycle splits, which enables us to show that the unimodular row considered by Suslin is completable, that is, the corresponding projective module is free. In order to show that the cocycle splits, we use Quillen’s splitting lemma and a result of Bhatwadekar–Lindel–Rao.
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Notes
- 1.
This assumption is needed to define cocycles.
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Acknowledgements
The authors would like to thank Professor Ravi A. Rao for his valuable support during this work. The authors would like to thank Professor Gopala Krishna Srinivasan for giving his time most generously and helping us make this paper more readable. The second named author would like to thank Professor Gopala Krishna Srinivasan for his support and advice during difficult times. The authors would also like to thank the referee for going through the paper carefully and pointing out some mistakes. The second named author also acknowledges the financial support from CSIR, which enabled him to pursue his doctoral studies.
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Sridharan, R., Yadav, S.K. (2020). On a Theorem of Suslin. In: Ambily, A., Hazrat, R., Sury, B. (eds) Leavitt Path Algebras and Classical K-Theory. Indian Statistical Institute Series. Springer, Singapore. https://doi.org/10.1007/978-981-15-1611-5_14
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DOI: https://doi.org/10.1007/978-981-15-1611-5_14
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