Are covering (enveloping) morphisms minimal?期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Are covering (enveloping) morphisms minimal?

Authors:	Edgar E Enochs J R Garcí a Rozas Luis Oyonarte

Institution:	Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027 ; Departamento de Algebra y Análisis Matemático, University of Almería, 04120 Almería, Spain ; Departamento de Algebra y Análisis Matemático, University of Almería, 04120 Almería, Spain

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.

Keywords:	Essential submodule superfluous submodule cover envelope minimal homomorphism covering homomorphism enveloping homomorphism

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