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Morita Equivalence and Morita Duality for Rings with Local Units and the Subcategory of Projective Unitary Modules

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Abstract

We study Morita equivalence and Morita duality for rings with local units. We extend Auslander’s results on the theory of Morita equivalence and the Azumaya–Morita duality theorem to rings with local units. As a consequence, we give a version of Morita theorem and Azumaya–Morita duality theorem over rings with local units in terms of their full subcategory of finitely generated projective unitary modules and full subcategory of finitely generated injective unitary modules.

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Acknowledgements

The authors would like to thank the referee for a careful reading of this paper and making helpful suggestions and comments that improved the paper.

Funding

The research of the first author was in part supported by a grant from IPM. Also, the research of the second author was in part supported by a grant from IPM (No. 14020416). The work of the second author is based upon research funded by Iran National Science Foundation (INSF) under Project No. 4001480.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441, Iran

    Alireza Nasr-Isfahani

  2. School of Mathematics, Institute for Research in Fundamental Sciences(IPM), Tehran, P.O. BOX:19395-5746, Iran

    Ziba Fazelpour & Alireza Nasr-Isfahani

Authors
  1. Ziba Fazelpour
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  2. Alireza Nasr-Isfahani
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The authors of this paper, ZF and AN-I, have contributed equally to the work and preparation of the manuscript.

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Correspondence to Alireza Nasr-Isfahani.

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Communicated by Lidia Angeleri Hügel.

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Fazelpour, Z., Nasr-Isfahani, A. Morita Equivalence and Morita Duality for Rings with Local Units and the Subcategory of Projective Unitary Modules. Appl Categor Struct 32, 10 (2024). https://doi.org/10.1007/s10485-024-09764-1

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