Are covering (enveloping) morphisms minimal?

Enochs, Edgar; García Rozas, J.; Oyonarte, Luis

doi:10.1090/S0002-9939-00-05339-9

Are covering (enveloping) morphisms minimal?
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by Edgar E. Enochs, J. R. García Rozas and Luis Oyonarte PDF

Proc. Amer. Math. Soc. 128 (2000), 2863-2868 Request permission

Abstract:

We prove that for certain classes of modules $\mathcal {F}$ such that direct sums of $\mathcal {F}$-covers ($\mathcal {F}$-envelopes) are $\mathcal {F}$-covers ($\mathcal {F}$-envelopes), $\mathcal {F}$-covering ($\mathcal {F}$-enveloping) 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 $\mathcal {F}$-covers are $\mathcal {F}$-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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