1. CMB Online first
 Gao, Zenghui

Homological Properties Relative to Injectively Resolving Subcategories
Let $\mathcal{E}$ be an injectively resolving subcategory of
left $R$modules. A left $R$module $M$
(resp. right $R$module $N$) is called $\mathcal{E}$injective
(resp. $\mathcal{E}$flat)
if $\operatorname{Ext}_R^1(G,M)=0$ (resp. $\operatorname{Tor}_1^R(N,G)=0$)
for any $G\in\mathcal{E}$.
Let $\mathcal{E}$ be a covering subcategory.
We prove that a left $R$module $M$ is $\mathcal{E}$injective
if and only if $M$ is a direct sum
of an injective left $R$module and a reduced $\mathcal{E}$injective
left $R$module.
Suppose $\mathcal{F}$ is a preenveloping subcategory of right
$R$modules such that
$\mathcal{E}^+\subseteq\mathcal{F}$ and $\mathcal{F}^+\subseteq\mathcal{E}$.
It is shown that a finitely presented right $R$module $M$ is
$\mathcal{E}$flat if and only if
$M$ is a cokernel of an $\mathcal{F}$preenvelope of a right
$R$module.
In addition, we introduce and investigate the
$\mathcal{E}$injective and $\mathcal{E}$flat dimensions of
modules and rings. We also introduce $\mathcal{E}$(semi)hereditary
rings and $\mathcal{E}$von Neumann regular rings and characterize
them in terms of $\mathcal{E}$injective and $\mathcal{E}$flat
modules.
Keywords:injectively resolving subcategory, \mathcal{E}injective module (dimension), \mathcal{E}flat module (dimension), cover, preenvelope, \mathcal{E}(semi)hereditary ring Categories:16E30, 16E10, 16E60 

2. CMB 2014 (vol 58 pp. 134)
3. CMB Online first
4. CMB 2013 (vol 57 pp. 318)
 Huang, Zhaoyong

Duality of Preenvelopes and Pure Injective Modules
Let $R$ be an arbitrary ring and $()^+=\operatorname{Hom}_{\mathbb{Z}}(,
\mathbb{Q}/\mathbb{Z})$ where $\mathbb{Z}$ is the ring of integers
and $\mathbb{Q}$ is the ring of rational numbers, and let
$\mathcal{C}$ be a subcategory of left $R$modules and $\mathcal{D}$
a subcategory of right $R$modules such that $X^+\in \mathcal{D}$
for any $X\in \mathcal{C}$ and all modules in $\mathcal{C}$ are pure
injective. Then a homomorphism $f: A\to C$ of left $R$modules with
$C\in \mathcal{C}$ is a $\mathcal{C}$(pre)envelope of $A$ provided
$f^+: C^+\to A^+$ is a $\mathcal{D}$(pre)cover of $A^+$. Some
applications of this result are given.
Keywords:(pre)envelopes, (pre)covers, duality, pure injective modules, character modules Categories:18G25, 16E30 
