JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (2): 79-84.doi: 10.6040/j.issn.1671-9352.0.2015.076

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Gorenstein injective objects in Abelian categories

CHENG Hai-xia, YIN Xiao-bin   

  1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui, China
  • Received:2015-02-27 Online:2016-02-16 Published:2016-03-11

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Abstract: 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.

Key words: precover, X -Gorenstein injective object, X -Gorenstein injective dimension

CLC Number: 

  • O154.2
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