%A CHENG Hai-xia, YIN Xiao-bin
%T Gorenstein injective objects in Abelian categories
%0 Journal Article
%D 2016
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2015.076
%P 79-84
%V 51
%N 2
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_2807.shtml}
%8 2016-02-16
%X Let A be an abelian category with enough injective objects and X a full subcategory of A. The definitions of X -Gorenstein injective object and YX -Gorenstein injective object are given, where YX={Y∈Ch(A)|Y is acyclic and KerdnY∈X. Under certain conditions, these two Gorenstein injective objects are related in a nice way. In particular, if I(A)⊆X, X∈Ch(A)is YX -Gorenstein injective if and only if Xi is X -Gorenstein injective for each i, when X is a self-orthogonal class. Subsequently, the relationships between X -Gorenstein injective dimension and YX -Gorenstein injective dimension are considered.