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Are covering (enveloping) morphisms minimal?


Authors: Edgar E. Enochs, J. R. García Rozas and Luis Oyonarte
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
Published electronically: March 29, 2000
MathSciNet review: 1664374
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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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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

DOI: https://doi.org/10.1090/S0002-9939-00-05339-9
Keywords: Essential submodule, superfluous submodule, cover, envelope, minimal homomorphism, covering homomorphism, enveloping homomorphism
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
Article copyright: © Copyright 2000 American Mathematical Society

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