Abstract
ABSTRACTLet R be an arbitrary ring with identity and M, a right R-module with Z2(M) the second singular submodule of M. We call an endomrphism φ of M, a t-automorphism if defined by is an isomorphism and we call M, a t-automorphism-invariant module if it is invariant under t-automorphisms of its injective hulls. This paper is devoted to investigation of various properties and characterizations of t-automorphism-invariant modules. We show that a module M is t-automorphism invariant if and only if every t-isomorphism between two t-essential submodules of M extends to an endomorphism of M.
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