正交类和相对Gorenstein模

Orthogonal Classes and Relative Gorenstein Modules

中文关键词:  Gorenstein模  正交类  对偶对  Mittag-Leffler条件

英文关键词:Gorenstein module  orthogonal class  duality pair  Mittag-Leffler condition

中文摘要:

      在这篇论文中,我们研究了$\mathcal{A}$-Gorenstein投射模类和$\mathcal{A}$的左正交模类之间的关系,以及$\mathcal{A}$-Gorenstein内射模类和A的右正交模类之间的关系.我们得到了$\mathcal{A}$-Gorenstein投射模和$\mathcal{A}$-Gorenstein内射模的一些函子刻画.以完备对偶对为工具,我们讨论了$\mathcal{A}$-Gorenstein投射模和$\mathcal{B}$-Gorenstein平坦模之间的关系,并推广了一些已知结论.

英文摘要:

      In this paper, we study the relations between the class of $\mathcal{A}$-Gorenstein projective modules and the left orthogonal class of $\mathcal{A}$, also the relations between the class of $\mathcal{A}$-Gorenstein injective modules and the right orthogonal class of $\mathcal{A}$. Some functor characterizations of $\mathcal{A}$-Gorenstein projective modules and $\mathcal{A}$-Gorenstein injective modules are obtained. Using the notion of complete duality pair, we discuss the relations between $\mathcal{A}$-Gorenstein projective modules and $\mathcal{B}$-Gorenstein flat modules. Some known results are generalized.