On Covers and Envelopes in Some Functor Categories |
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Authors: | Lixin Mao |
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Affiliation: | 1. Institute of Mathematics , Nanjing Institute of Technology , Nanjing , China maolx2@hotmail.com |
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Abstract: | We study the existence of covers and envelopes by some special functors on the category of finitely presented modules. As an application, we characterize some important rings using these functors. We also investigate homological properties of some functors on the stable module category. The relationship between phantoms and Ext-phantoms is obtained. It is shown that every left R-module M has an Ext-phantom preenvelope f: M → N with coker(f) pure-projective. Finally, we prove that, as a torsionfree class of (mod-R, Ab), (mod-R, Ab) is generated by the FP-injective objects. |
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Keywords: | Cotorsion functor Cotorsion pair Ext-phantom Flat functor FP-injective functor FP-projective functor Phantom (Pre)envelope (Pre)cover Torsion theory |
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