BONGARTZ τ-COMPLEMENTS OVER SPLIT-BY-NILPOTENT EXTENSIONS
Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 461-470

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Let C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E, and let M be a τC-rigid module with U its Bongartz τC-complement. If the induced module, M ⊗CB, is τB-rigid, we give a necessary and sufficient condition for U ⊗CB to be its Bongartz τB-complement. If M is τB-rigid, we again provide a necessary and sufficient condition for U ⊗CB to be its Bongartz τB-complement.
ZITO, STEPHEN. BONGARTZ τ-COMPLEMENTS OVER SPLIT-BY-NILPOTENT EXTENSIONS. Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 461-470. doi: 10.1017/S0017089518000290
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[1] 1. Adachi, T., Iyama, O. and Reiten, I., τ-tilting theory, Compos. Math. 150 (3) (2014), 415–452. Google Scholar

[2] 2. Assem, I. and Marmaridis, N., Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998), 1547–1555. Google Scholar

[3] 3. Assem, I., Simson, D. and Skowronski, A., Elements of the representation theory of associative algebras, 1: Techniques of representation theory, London Mathematical Society Student Texts 65 (Cambridge University Press, 2006). Google Scholar

[4] 4. Assem, I. and Zacharia, D., Full embeddings of almost split sequences over split-by-nilpotent extensions, Coll. Math. 81 (1) (1999), 21–31. Google Scholar

[5] 5. Auslander, M. and Smalø, S. O., Almost split sequences in subcategories, J. Algebra 69 (2) (1981), 426–454. Google Scholar

[6] 6. Schiffler, R. and Serhiyenko, K., Induced and coinduced modules in cluster-tilted algebras, J. Algebra 472 (2017), 226–258. Google Scholar

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