Abstract
In this paper, we construct a local artinian ring R with Jacobson radical W such that \(W^2=0\), \(Q=R/W\) is commutative, dim\((_QW)=1\) and dim\((W_Q)=2\). Then we show that, for this ring R, the category of all right R-modules Mod-R is not a Baer–Kaplansky class by proving that the class of all indecomposable right R-modules (all finitely generated right R-modules) is not Baer-Kaplansky. Finally, we give an application on some module classes over this constructed ring R.
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Acknowledgements
This paper is a part of the Master Thesis of the second author. She would like to thank TUBITAK (The Scientific and Technological Research Coincil of Türkiye) for their financial support under the MSc. Program “2210-A General National Scholarship”. The authors also thank Professor Alberto Facchini for his valuable comments on Example 2.1.
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Keskin Tütüncü, D., Başer, Z. An investigation of the Baer–Kaplansky property. São Paulo J. Math. Sci. (2024). https://doi.org/10.1007/s40863-024-00407-w
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DOI: https://doi.org/10.1007/s40863-024-00407-w