形式三角矩阵环上的Clean-投射模与Clean-奇点范畴

Clean-Projective Modules and Clean-Singularity Categories over Formal Triangular Matrix Rings

摘要

设$T=\left(\begin{array}{cc} R & M \\ 0 & S \end{array}\right) $是形式三角矩阵环.首先,考虑T上的clean-投射模,证明若左T-模(X,Y)_φ是clean-投射模,则X/(Imφ)是clean-投射左R-模,Y是clean-投射左S-模;其次,分别构造T上的clean-导出范畴和clean-奇点范畴的粘合.

Abstract

Let $T=\left(\begin{array}{cc} R & M \\ 0 & S \end{array}\right) $ be a formal triangular matrix ring. First, this paper investigates clean-projective modules over T, and proves that if a left T-module (X,Y)_ϕ is clean-projective, then X/(Im ϕ) is a clean-projective left R-module and Y is a clean-projective left S-module. Second, the recollements for clean-derived categories and clean-singularity categories over T are constructed separately.

关键词

形式三角矩阵环 / clean-投射模 / clean-奇点范畴 / 粘合

Key words

formal triangular matrix ring / clean-projective module / clean-singularity category / recollement

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基金资助

国家自然科学基金(12071120)

山西省高等学校科技创新项目(2025L092)