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Lifting properties of formal triangular matrix rings

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This article concerns various lifting properties of formal triangular matrix rings. The first aim is to study idempotent lifting ideals of formal triangular matrix rings. In connection with the idempotent lifting property, we also describe strong lifting, enabling and fully lifting ideals of formal triangular matrix rings. Moreover, we give a description for an ideal of a triangular matrix ring to be (idempotent) stable range one lifting. Finally, we consider other forms of lifting ideals including regular lifting, unit lifting, unit-regular lifting and clean lifting ideals for a formal triangular matrix ring, and highlight our results by providing several examples.

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Acknowledgements

I would like to thank the anonymous referees for very careful reading of the manuscript, for many useful comments and corrections, and for suggesting Definition 2.3 and Theorem 2.4 which simplified the presentation and improved the quality of the paper.

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  1. Department of Mathematics, Hacettepe University, 06800, Beytepe, Ankara, Turkey

    Meltem Altun Özarslan

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  1. Meltem Altun Özarslan
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Correspondence to Meltem Altun Özarslan.

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Altun Özarslan, M. Lifting properties of formal triangular matrix rings. RACSAM 115, 104 (2021). https://doi.org/10.1007/s13398-021-01044-0

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