Phantom Envelopes and $$\mathrm{Ext}$$ -Phantom Covers of Modules
Tóm tắt
We first prove that if a monomorphism is a phantom envelope of a left R-module, then its cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an $$\mathrm{Ext}$$-phantom cover of a left R-module, then its kernel is pure-injective. Second, we characterize several rings such as left FC rings and left semihereditary rings using phantom envelopes and $$\mathrm{Ext}$$-phantom covers of modules.
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