Şahinkaya, SerapQuynh, Truong Cong2025-03-172025-03-1720211222-9016https://doi.org/10.24193/mathcluj.2021.1.11https://hdl.handle.net/20.500.13099/1455A module theoretic notion of annihilator-stable rings is defined and some characterizations of it are studied. A module M is called kernel-stable if every element α ∈ End(M) satisfies the following condition: if α(M) + Kerβ = M, β ∈ End(M), then (α − γ)(m) ∈Kerβ for an automorphism γ of M and for all m ∈ M. For a pseudo-semi-projective module M, this notion is equivalent to that of uniquely generated module. © 2021, Publishing House of the Romanian Academy. All rights reserved.eninfo:eu-repo/semantics/openAccessAnnihilator-stable ringsKernel-stable modulesMatrix ringsPseudo-semiprojective moduleStable rangeUniquely generated modulesUnit-regular ringsVon Neumann regular ringsArticle10.24193/mathcluj.2021.1.116311191272-s2.0-85122042154Q4