Gorenstein injective covers and envelopes over noetherian rings
Gorenstein injective covers and envelopes over noetherian rings
复制标题
DOI：
10.1090/s0002-9939-2014-12232-5
复制
发表时间：
2014-08
期刊：
影响因子：
2.4
通讯作者：
E. Enochs;A. Iacob
中科院分区：
文献类型：
--
作者：
E. Enochs;A. Iacob
证明了：若R是交换Noether环，使得Gorenstein内射模的特征模是Gorenstein平坦的，则Gorenstein内射模类在直极限下闭，并且是覆盖的.我们还证明了在这样的环上Gorenstein内射模类是包络的。特别是这表明存在的Gorenstein内射信封交换诺特环对偶复合物。
We prove that if R is a commutative noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat, then the class of Gorenstein injective modules is closed under direct limits and it is covering. We also prove that over such a ring the class of Gorenstein injective modules is enveloping. In particular this shows the existence of the Gorenstein injective envelopes over commutative noetherian rings with dualizing complexes.