The existence of relative pure injective envelopes

Injective Envelopes of Banach Spaces

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...

Injective Envelopes of Separable C * -algebras

Characterisations of those separable C∗-algebras that have type I injective envelopes or W∗-algebra injective envelopes are presented. An operator system I is injective if for every inclusion E ⊂ F of operator systems each completely positive linear map ω : E → I has a completely positive extension to F . An injective envelope of an operator system E is an injective operator system I such that ...

Injective Envelopes and Projective Covers of Quivers

This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.

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...