Fusible Modules: Structure, Algoritmic Decomposition and Extensions
Keywords:
Fusible modules, $\delta$-fusible modules, Torsion and torsion-free modules, Lifting and extending modules, Endomorphism ringsAbstract
Fusible modules generalize the notion of fusibility from ring theory to module theory, linking torsion theory, nonsingularity, and endomorphism structures. We study various classes, including regular, unit, S-fusible, right fusible, and $\delta$-fusible modules, and analyze their stability under submodules, direct sums, quotients, extensions, tensor products, and Hom-functors.
We investigate fusible endomorphisms and endomorphism rings, provide algorithmic decomposition procedures for modules and matrices, and present new criteria, examples, and counterexamples illustrating strict inclusions among module classes. Connections with lifting, extending, and partially injective modules are highlighted. Applications to matrix rings, group algebras, and crossed products showcase the theoretical and computational utility of fusible modules.
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References
1] F. W. Anderson and K. R. Fuller. Rings and Categories of Modules. Springer-Verlag, New York, 2nd edition, 1992. 2
[2] I. Baydar, B. Ungor, S. Halicioglu, and A. Harmanci. Fusible modules. Hacettepe Journal of Mathematics and Statistics, 53(3):714–723, 2024. 1, 2, 3, 3, 4.2, 4.4, 2
[3] I. Baydar, B. Ungor, S. Halicioglu, and A. Harmanci. Modules whose endomorphism rings are fusible. Communications in Algebra, 2025. 1, 5, 5.1, 5.3
[4] P. Bhattacharjee, W. W. McGovern, and Y. Zhou. On fusible rings and related notions. Communications in Algebra, 53(2):842–853, 2025. 1
[5] P. Bhattacharjee, W. W. McGovern, and Y. Zhou. Unit-fusible property via regularity. Mediterranean Journal of Mathematics, 22:136, 2025. 1, 2, 10
[6] M. Es-saidi, N. Mahdou, and U. Tekir. S-fusible rings. Beitr¨age zur Algebra und Geometrie / Contributions to Algebra and Geometry, 66(1):5–18, 2025. 1, 10
[7] E. Ghashghaei and W. W. McGovern. Fusible rings. Communications in Algebra, 45(3):1151–1165, 2017. 1
[8] G. Gumusel, M. T. Kosan, and J. Zemlicka. On fusible rings. Communications in Algebra, 51(9):3764–3767, 2023. 1
[9] S. Higuera and A. Reyes. A survey on the fusible property of skew pbw extensions. Journal of Algebraic Systems, 2022. 1
[10] M. T. Kosan and J. Matczuk. On fusible rings. Communications in Algebra, 47(9):3789–3793, 2019. 1
[11] T. Y. Lam. Lectures on Modules and Rings, volume 189 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1999. 2
[12] O. A. Naji, M. Ozen, U. Tekir, and S. Koc. On regular fusible moddules. Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A, Matem´aticas, 119(1), 2025. 1, 2, 3.
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Copyright (c) 2026 Abdelkader Hamdouni
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