论文标题
gorenstein物体在阿贝尔类别的N-平地扩展中
Gorenstein objects in the n-Trivial extensions of abelian categories
论文作者
论文摘要
考虑到Abelian类别，我们通过定义新的特殊对象类别，引入了（强烈）Gorenstein投射（分别，注射式）对象的（强烈）投射（分别，注射式）对象的概念。然后，我们研究这些特性转移到Abelian类别及其N-平地扩展类别时的转移，并在其上赋予Gorenstein对象的表征。最后，我们将这项研究的应用在关联环和三角形矩阵环上的模块类别上。
Given an abelian category, we introduce a categorical concept of (strongly) Gorenstein projective (resp., injective) objects, by defining a new special class of objects. Then we study the transfer of these properties when passing to an abelian category and its n-trivial extension category and also give a characterization of Gorenstein object over it. We give, at the end, applications of this study on the category of modules over an associative ring and triangular matrix rings.
