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Zariski cancellation problem for non-domain noncommutative algebras

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Abstract

We study Zariski cancellation problem for noncommutative algebras that are not necessarily domains.

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Acknowledgements

The authors thank the referee for his/her very careful reading and valuable comments and for allowing them to include Remark 5.5 in this paper. The authors thank Ken Goodearl and Daniel Krashen for many useful conversations on the subject, and thank Ken Goodearl for suggesting the term “retractable” in Definition 2.1 and Lance Small for providing the references [7, 29]. O. Lezama was partially supported by Universidad Nacional de Colombia (HERMES code 40482). Y.H. Wang was partially supported by the Nature Science Foundation of China (No.11871071), the Foundation of China Scholarship Council (Grant no. [2016]3099), the Foundation of Shanghai Science and Technology Committee (Grant no. 15511107300), the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars of Ministry of Education of China and the Innovation program of Shanghai Municipal Education Commission (no. 15ZZ037). J.J. Zhang was partially supported by the US National Science Foundation (nos. DMS-1402863 and DMS-1700825).

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Correspondence to J. J. Zhang.

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Lezama, O., Wang, Y. & Zhang, J.J. Zariski cancellation problem for non-domain noncommutative algebras. Math. Z. 292, 1269–1290 (2019) doi:10.1007/s00209-018-2153-7

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Keyword

  • Zariski cancellation problem

Mathematics Subject Classification

  • Primary 16P99
  • 16W99