Abstract
The notion of a nilpotent-invariant module was introduced and thoroughly investigated in Koşan and Quynh (Comm. Algebra 45, 2775–2782 2017) as a proper extension of an automorphism-invariant module. In this paper a ring is called a right \(\mathfrak {n}\)-ring if every right ideal is nilpotent-invariant. We show that a right \(\mathfrak {n}\)-ring is the direct sum of a square full semisimple artinian ring and a right square-free ring. Moreover, right \(\mathfrak {n}\)-rings are shown to be stably finite, and if the ring is also an exchange ring then it satisfies the substitution property, has stable range 1. These results are non-trivial extensions of similar ones on rings every right ideal is automorphism-invariant.
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Acknowledgements
The authors would like to thank the referee for the valuable suggestions and comments. The second author would like to thank the Funds for Science and Technology Development of the Ministry of Education and Training under the Project Number B2023.DNA.14.
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Dedicated to Professor Ngo Viet Trung on his seventieth birthday.
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Quynh, T.C., Van, T.T.T. On Nilpotent-invariant One-sided Ideals. Acta Math Vietnam (2024). https://doi.org/10.1007/s40306-024-00524-w
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DOI: https://doi.org/10.1007/s40306-024-00524-w