Injective and flat covers, envelopes and resolvents
Injective and flat covers, envelopes and resolvents
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DOI：
10.1007/bf02760849
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发表时间：
1981-09
影响因子：
1
通讯作者：
E. Enochs
中科院分区：
文献类型：
--
作者：
E. Enochs
使用内射包络的范畴定义的对偶，可以定义内射覆盖。对环R，证明了每个左R-模都有内射覆盖当且仅当R是左诺特环。定义了平坦包络，并证明对于2维规则局部环上的所有模块都存在平坦包络。利用内射覆盖，可以定义极小内射预解式。
Using the dual of a categorical definition of an injective envelope, injective covers can be defined. For a ringR, every leftR-module is shown to have an injective cover if and only ifRis left noetherian. Flat envelopes are defined and shown to exist for all modules over a regular local ring of dimension 2. Using injective covers, minimal injective resolvents can be defined.