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Beaumont studied groups with isomorphic proper subgroups (see Beaumont: Bull Amer Math Soc 51, 381–387 1945 [1]). In Beaumont et al.: Trans Amer Math Soc 91(2), 209–219 1959 [2], Beaumont and Pierce consider the problem of determining all R-modules M over a principal ideal domain R which have proper isomorphic submodules. Such modules are called I-modules. In Chaturvedi: Iso-retractable Modules and Rings (to appear) [3], we investigate iso-retractable modules that is the modules which are isomorphic to their nonzero submodules. Also, a ring R is said to be iso-retractable if \(R_R\) is an iso-retractable module. The class of iso-retractable modules lies in between simple modules and the uniform modules. In the present paper, our main objective is to investigate general properties of iso-retractable modules and rings. Finally, we show that being iso-retractable is a Morita invariant property. |
