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.References
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Additional Information
- Edgar E. Enochs
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
- Email: enochs@ms.uky.edu
- J. R. García Rozas
- Affiliation: Departamento de Algebra y Análisis Matemático, University of Almería, 04120 Almería, Spain
- Email: jrgrozas@ualm.es
- Luis Oyonarte
- Affiliation: Departamento de Algebra y Análisis Matemático, University of Almería, 04120 Almería, Spain
- Email: loyonart@ualm.es
- Received by editor(s): April 21, 1998
- Received by editor(s) in revised form: November 14, 1998
- Published electronically: March 29, 2000
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2863-2868
- MSC (2000): Primary 16D10; Secondary 16D40, 13H99
- DOI: https://doi.org/10.1090/S0002-9939-00-05339-9
- MathSciNet review: 1664374