Generalized Pure Modules

Generalized Derivations on Modules

Superdecomposable pure-injective modules

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations. We describe the relation in terms of pointed modules. We present methods for producing superdecomposable pure-injectives and give some details of recent work of Harland doing this in the context of tubular algebras. 2010 Mathematics Subject Classification. Primary 16G...

Pure-injective modules

The pure-injective R-modules are defined easily enough: as those modules which are injective over all pure embeddings, where an embedding A → B is said to be pure if every finite system of R-linear equations with constants from A and a solution in B has a solution in A. But the definition itself gives no indication of the rich theory around purity and pure-injectivity. The purpose of this surve...

Definition of Pure Hodge Modules

(3) A good filtration F•M by OX -coherent subsheaves of M, such that FpM · FkD ⊂ Fp+kM and such that gr• M is coherent over gr• DX ' Sym • TX . Its Tate twist is defined by M(k) = (M, F•−kM,K ⊗Q Q(k)) where Q(k) = (2πi)Q ⊂ C. For a given function f : X → C, we want to define the nearby and vanishing cycles, denoted ψf and φf , in the category of filtered regular holonomic D-modules with Q-struc...

Pure Submodules of Multiplication Modules

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...