Abstract
We prove that for certain classes of modules F such that direct sums of F-covers (F-envelopes) are F-covers (F-envelopes), F-covering (Fenveloping) homomorphisms are always right (left) minimal. As a particular case we see that over noetherian rings, essential monomorphisms are left minimal. The same type of results are given when direct products of F-covers are F-covers. Finally we prove that over commutative noetherian rings, any direct product of flat covers of modules of finite length is a flat cover.
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