论文标题
$ k $的同源理论 - 双重型理想在偶性品种中的理想
Homological theory of $k$-idempotent ideals in dualizing varieties
论文作者
论文摘要
在这项工作中，我们发展了$ k $的理想理论在二元化品种的情况下。 M. Auslander，M。I。Platzeck和G. Todorov先前在\ Cite {Apg}中给出的几个结果已扩展到这种情况。给定理想的$ \ Mathcal {i} $（这是一个投影模块的痕迹），我们构建了一个规范的回忆，这是对Artin代数的模块类别中众所周知的回忆的类似物。此外，我们研究了这种回忆中涉及的类别的同源性能。因此，我们在理想的$ \ Mathcal {i} $上找到条件，以在这种回忆中获得Quasi Herditary代数。还提供了对有限派生类别的应用程序。
In this work, we develop the theory of $k$-idempotent ideals in the setting of dualizing varieties. Several results given previously in \cite{APG} by M. Auslander, M. I. Platzeck, and G. Todorov are extended to this context. Given an ideal $\mathcal{I}$ (which is the trace of a projective module), we construct a canonical recollement which is the analog to a well-known recollement in categories of modules over artin algebras. Moreover, we study the homological properties of the categories involved in such a recollement. Consequently, we find conditions on the ideal $\mathcal{I}$ to obtain quasi-hereditary algebras in such a recollement. Applications to bounded derived categories are also given.
