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- W2034373740 abstract "An R-module M is called strongly Hopfian (respectively strongly co-Hopfian) if for every endomorphism f of M the chain Kerf⊆Kerf2⊆⋯ (respectively Imf⊇Imf2⊇⋯) stabilizes. The class of strongly Hopfian (respectively co-Hopfian) modules lies properly between the class of Noetherian (respectively Artinian) and the class of Hopfian (respectively co-Hopfian) modules. For a quasi-projective (respectively quasi-injective) module, M, if M is strongly co-Hopfian (respectively strongly Hopfian) then M is strongly Hopfian (respectively strongly co-Hopfian). As a consequence we obtain a version of Hopkins–Levitzki theorem for strongly co-Hopfian rings. Namely, a strongly co-Hopfian ring is strongly Hopfian. Also we prove that for a commutative ring A, the polynomial ring A[X] is strongly Hopfian if and only if A is strongly Hopfian." @default.
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- W2034373740 date "2007-02-01" @default.
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- W2034373740 title "Generalized Fitting modules and rings" @default.
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- W2034373740 doi "https://doi.org/10.1016/j.jalgebra.2006.07.010" @default.
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