Abstract
We prove an algebraic analogue of the Mayer–Vietoris sequence for cohomology for the part of the sequence corresponding to the zeroth and first cohomology. We also prove a result which gives an indication of how one should continue this sequence to include the second cohomology groups in the case of rings of dimension 2.
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Acknowledgements
The authors would like to thank Professor Ravi A. Rao for his valuable support during this work and for bringing to our attention the crucial lemma of Vaserstein used in Sect. 15.5. 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 third named author would like to thank Professor Gopala Krishna Srinivasan for his support and advice during difficult times. The third named author also acknowledges the financial support from CSIR, which enabled him to pursue his doctoral studies.
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Sridharan, R., Upadhyay, S.K., Yadav, S.K. (2020). On an Algebraic Analogue of the Mayer–Vietoris Sequence. 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_15
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DOI: https://doi.org/10.1007/978-981-15-1611-5_15
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