Let R be an arbitrary ring with identity and M a right R-module with S= End R (M). Let F be a
fully invariant submodule of M and I− 1 (F) denotes the set {m∈ M: Im⊆ F} for any subset I of …

Let R be an arbitrary ring with identity and M a right R-module with S= End (R)(M). Let F be a
fully invariant submodule of M and I-1 (F) denotes the set {m is an element of M: Im subset of …

© 2017 Taylor & Francis. Let R be an arbitrary ring with identity and M a right R-module with
S= EndR (M). Let F be a fully invariant submodule of M and I− 1 (F) denotes the set {m∈ M …

Proof. By [3, 7.11], an R-module M is extending if and only if M= Z2 (M)⊕ M′ for some
submodule M′ of M such that M′ and Z2 (M) are both extending and Z2 (M) is M …

Let R be an arbitrary ring with identity and M a right R-module with S= End (R)(M). Let F be a
fully invariant submodule of M and I-1 (F) denotes the set {m is an element of M: Im subset of …

Let R be an arbitrary ring with identity and M a right R-module with S= End (R)(M). Let F be a
fully invariant submodule of M and I-1 (F) denotes the set {m is an element of M: Im subset of …