Page 1 PURE AND APPLIED MATHEMATICS A Series of Monographs and Textbooks LINEAR
ALGEBRA OVER COMMUTATIVE RINGS Bernard R. McDonald Page 2 Linear Algebra Over …

We prove the relative Grauert-Riemenschneider vanishing, Kawamata-Viehweg vanishing,
and Koll\'ar injectivity theorems for proper morphisms of schemes of equal characteristic …

We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac–
Moody algebras. The main new tool is a relation between moment graphs and finite …

In this paper we will first establish a duality between in jectivity and flatness for modules.
That is: Let E be a faithfully in jective module". Then, for each module A, we have W, dim. A …

We study the following question: Given two semidualizing complexes 𝐵 and 𝐶 over a
commutative noetherian ring 𝑅, does the vanishing of Ext R n (B, C) for 𝑛≫ 0 imply that 𝐵 is …

Let R be a commutative ring, M an R-module and φ a be the endomorphism of M given by
right multiplication by a∈ R. We say that M is weakly-morphic if M/φ a (M)≅ ker (φ a) as R …

In this paper, we prove that the injective cover of the R-module E (R/B)/R/B for a prime ideal
B of R is the direct sum of copies of E (R/B) for prime ideals D⊃ B, and if B is maximal, the …

We study the transfer of (dual) relative CS-Rickart properties via functors between abelian
categories. We consider fully faithful functors as well as adjoint pairs of functors. We give …

All rings considered are commutative. In this article we introduce and study two notions of
modules which are stronger than CS modules, namely weakly IN modules and strongly CS …

We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-
Moody algebras. The main new tool is a relation between moment graphs and finite …