Abelian范畴中Gorenstein内射对象

doi:10.6040/j.issn.1671-9352.0.2015.076

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 79-84.doi: 10.6040/j.issn.1671-9352.0.2015.076

Abelian范畴中Gorenstein内射对象

程海霞,殷晓斌

安徽师范大学数学计算机科学学院, 安徽芜湖 241000

收稿日期:2015-02-27 出版日期:2016-02-16 发布日期:2016-03-11
作者简介:程海霞(1979— ), 女, 博士, 讲师, 研究方向为同调代数. E-mail:c701332@mail.ahnu.edu.cn
基金资助:
2011年国家自然科学基金研究项目(11071097);2014年安徽师范大学博士科研资助项目(071406)

Gorenstein injective objects in Abelian categories

CHENG Hai-xia, YIN Xiao-bin

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

摘要/Abstract

摘要： 给出了Abelian范畴A和复形范畴Ch(A)中X -Gorenstein内射对象及Y_X -Gorenstein内射对象的定义, 其中X ⊆A, Y_X={Y∈Ch(A)|Y是正合复形且Kerdⁿ_Y ∈X }。研究了这两类Gorenstein内射对象的同调性质及它们的区别和联系。证明了若X是包含所有内射对象的自正交的满子范畴, 则X∈Ch(A)是Y_X -Gorenstein内射的当且仅当Xⁱ都是X -Gorenstein内射的。在此基础上研究了两类范畴中X -Gorenstein内射维数和Y_X -Gorenstein内射维数以及它们之间的关系。在一定的条件下, Y_X -G I dim(X)=Sup{X -G I dim(Xⁱ)|i∈Z}。

关键词: 预覆盖, X -Gorenstein内射维数, X -Gorenstein内射对象

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 Y_X -Gorenstein injective object are given, where Y_X={Y∈Ch(A)|Y is acyclic and Kerdn_Y∈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 Y_X -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 Y_X -Gorenstein injective dimension are considered.

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

中图分类号:

O154.2

程海霞,殷晓斌. Abelian范畴中Gorenstein内射对象[J]. 山东大学学报（理学版）, 2016, 51(2): 79-84.

CHENG Hai-xia, YIN Xiao-bin. Gorenstein injective objects in Abelian categories[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 79-84.

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Abelian范畴中Gorenstein内射对象

Gorenstein injective objects in Abelian categories

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