In this paper we investigate whether the class of (strongly) FI-lifting modules are closed under particular class of submodules, direct summands and direct sums.
📌 3 Key Takeaways
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Objective & Hypothesis:A module M is called lifting if every submodule A of M contains a direct summand B of M such that Bce,→ A in M.
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Key Findings & Data:We call M is (strongly) FIlifting if every fully invariant submodule A of M contains a (fully invariant) direct summand B of M such that Bce,→ A in M.
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Conclusion & Impact:In this paper we investigate whether the class of (strongly) FI-lifting modules are closed under particular class of submodules, direct summands and direct sums.
A module M is called lifting if every submodule A of M contains a direct summand B of M such that Bce,→ A in M. We call M is (strongly) FIlifting if every fully invariant submodule A of M contains a (fully invariant) direct summand B of M such that Bce,→ A in M. The class of FI-lifting modules properly contains the class of lifting modules and the class of strongly FI-lifting modules. But a strongly FI-lifting module need not be a lifting module and vice versa. In this paper we investigate whether the class of (strongly) FI-lifting modules are closed under particular class of submodules, direct summands and direct sums.