The Singular Ideal and the Socle of Incidence Algebras

投射化解析与 incidence 代数的霍奇斯同调

Projective resolutions of simple modules and Hochschild cohomology for incidence algebras

本文提出计算有限维 incidence 代数Λ简单模投射化解析的算法方法，并应用于计算Ext群、霍奇斯同调群和有限T0拓扑空间的奇异同调群。

On derived equivalences of lines, rectangles and triangles

We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor products, allowing us to obtain many derived equivalences that have not been observed by using previous techniques. Particular examples include algebras generalizing the ADE-chain related to singularity theory, incidence algebras of posets and certain Auslander algebras or more generally endomorphism algebras of initial preprojective modules over path algebras of …

非交换环中极大子环的经典理想理论

Classical ideals theory of maximal subrings in non-commutative rings

本文研究非交换环中极大子环扩张下若干重要理想（如根、基座、奇异理想）的关系，给出特定条件下（如约化环、左阿廷环）的精确刻画与结构分解。