Relative copure injective and copure flat modules |
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Authors: | Lixin Mao Nanqing Ding |
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Institution: | a Department of Mathematics, Nanjing University, Nanjing 210093, PR China b Department of Basic Courses, Nanjing Institute of Technology, Nanjing 211167, PR China |
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Abstract: | Let R be a ring, n a fixed nonnegative integer and In (Fn) the class of all left (right) R-modules of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n-copure injective (resp., n-copure flat) if (resp., ) for any N∈In. It is shown that a left R-module M over any ring R is n-copure injective if and only if M is a kernel of an In-precover f:A→B of a left R-module B with A injective. For a left coherent ring R, it is proven that every right R-module has an Fn-preenvelope, and a finitely presented right R-module M is n-copure flat if and only if M is a cokernel of an Fn-preenvelope K→F of a right R-module K with F flat. These classes of modules are also used to construct cotorsion theories and to characterize the global dimension of a ring under suitable conditions. |
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Keywords: | 16E10 16D50 16D40 |
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