1. Strongly Gorenstein AC-injective complexes and dimensions(强Gorenstein AC-内射复形及维数)
- Author
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汪鑫(WANG Xin) and 卢博(LU Bo)
- Subjects
strongly gorenstein ac-injective complex(强gorenstein ac-内射复形) ,gorenstein ac-injective module(gorenstein ac-内射模) ,dg-absolutely clean complex(dg-绝对clean复形) ,dimension(维数) ,Electronic computers. Computer science ,QA75.5-76.95 ,Physics ,QC1-999 - Abstract
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.(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。)
- Published
- 2024
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