Displaying similar documents to “Almost-flat modules”

The existence of envelopes

Edgar E. Enochs, Overtoun M. G. Jenda, Jinzhong Xu (1993)

Rendiconti del Seminario Matematico della Università di Padova

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Precovers

Ladislav Bican, Blas Torrecillas (2003)

Czechoslovak Mathematical Journal

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Let 𝒢 be an abstract class (closed under isomorpic copies) of left R -modules. In the first part of the paper some sufficient conditions under which 𝒢 is a precover class are given. The next section studies the 𝒢 -precovers which are 𝒢 -covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left R -modules. Especially, several sufficient conditions for the existence of σ -torsionfree and σ -torsionfree σ -injective covers are presented. ...

Copure injective resolutions, flat resolvents and dimensions

Edgar E. Enochs, Jenda M. G. Overtoun (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize n -Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring R has cokernels (respectively kernels), then R is 2 -Gorenstein.