强Gorenstein AC-内射复形及维数OA北大核心CSTPCD
Strongly Gorenstein AC-injective complexes and dimensions
设n为任意整数,引入并研究了强Gorenstein AC-内射复形,证明了复形X是强Gorenstein AC-内射复形当且仅当Xn是Gorenstein AC-内射模,且对任意的DG-绝对clean复形A,复形同态f:A→X是零伦的.特别地,若X为有界正合复形,则X的强Gorenstein AC-内射性等价于模Zn(X)的Gorenstein AC-内射性,也等价于模Xn的Gorenstein AC-内射性.此外,引入并研究了复形的强Gorenstein AC-内射维数.
Let n be any integer.The notion of strongly Gorenstein AC-injective complexes is introduced and studied.It is proven that a complex X is strongly Gorenstein AC-injective if and only if each Xn is a Gorenstein AC-injective module and any homomorphism f:A→X is null homotopic whenever A is a DG-absolutely clean complex.In particular,if a complex X is bounded and exact,then the strongly Gorenstein AC-injectivity of a complex X is equivalent to the Gorenstein AC-injectivity of the module Zn(X),and is also equivalent to the Gorenstein AC-injectivity of the module Xn.In addition,the notion of strongly Gorenstein AC-injective dimension of complexes is introduced and studied.
汪鑫;卢博
西北民族大学 数学与计算机科学学院,甘肃 兰州 730030
数学
强Gorenstein AC-内射复形Gorenstein AC-内射模DG-绝对clean复形维数
strongly Gorenstein AC-injective complexGorenstein AC-injective moduleDG-absolutely clean complexdimension
《浙江大学学报（理学版）》 2024 (004)
426-433 / 8
中央高校基本科研业务经费(31920230173);国家自然科学基金资助项目(12061061);甘肃省第一批陇原青年英才项目.
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