Abstract
A right R-module M is called: (1) retractable if \({{\,\mathrm{Hom}\,}}_R(M, N) \ne 0\) for any non-zero submodule N of M; (2) coretractable if \({{\,\mathrm{Hom}\,}}_R(M/N, M)\ne 0\) for any proper submodule N of M. It shows that if M is locally noetherian and every nonzero module in the category \(\sigma [M]\) has a maximal submodule, then the retractability and coretractability of modules in \(\sigma [M]\) coincide. Let C be a coalgebra over a field k. We prove that all right C-comodules are retractable if and only if every right C-comodule is coretractable.
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The work of A.N. Abyzov was performed under the development program of Volga Region Mathematical Center (agreement no. 075-02-2021-1393).
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Abyzov, A.N., Eryashkin, M.S. Retractable and coretractable modules in Wisbauer category. Beitr Algebra Geom 63, 639–645 (2022). https://doi.org/10.1007/s13366-021-00591-2
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DOI: https://doi.org/10.1007/s13366-021-00591-2