Abstract
Let R be any ring, M an R-module and G a subgroup of \(\hbox {Aut}_{\mathrm{R}}\hbox {M}\) of finite rank. We compare the R-module structure of certain R-G images of M with that of certain R-G submodules of M. (We are treating M here as an R-G bimodule). For example, if A \(=\) [M, G] and \(\hbox {B}=\hbox {M/C}_{\mathrm{M}}\hbox {(G)}\), then we prove that as R-modules, A is Artinian if B is Artinian, B is Noetherian if A is Noetherian and hence A has a composition series of finite length if and only if B does.
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Wehrfritz, B.A.F. Groups of module automorphisms of finite rank. Rend. Circ. Mat. Palermo, II. Ser 66, 285–294 (2017). https://doi.org/10.1007/s12215-016-0252-z
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DOI: https://doi.org/10.1007/s12215-016-0252-z