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- W2162655953 abstract "We call a module R M essentially retractable if HomR( ) ,0 MN ≠ for all essential submodules N of M. For a right FBN ring R, it is shown that: (i) A nonzero module R M is retractable (in the sense that HomR( ) ,0 MN ≠ for all nonzero R M N ≤ ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii) A non-zero module R M is essentially retractable if and only if there exists a prime ideal () R M Ass P∈ such that HomR( ) ,0 MN ≠ . Over semiprime right nonsingular rings, a nonsingular essentially retractable module is precisely a module with nonzero dual. Moreover, over certain rings R, including right FBN rings, it is shown that a nonsingular module M with enough uniforms is essentially retractable if and only if there exist uniform retractable R-modules { } I i i U ∈ and R-homomorphisms M U M i I i ⎯→ ⎯ ⊕ ⎯→ ⎯ ∈ β α with 0 βα ≠ ." @default.
- W2162655953 created "2016-06-24" @default.
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- W2162655953 date "2007-12-01" @default.
- W2162655953 modified "2023-09-28" @default.
- W2162655953 title "ESSENTIALLY RETRACTABLE MODULES" @default.
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- W2162655953 doi "https://doi.org/10.22059/jsciences.2007.35080" @default.
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