X -GC -投射复形
X -GC -Projective Complexes
DOI: 10.12677/PM.2022.1210167, PDF, HTML,    国家自然科学基金支持
作者: 李星宇, 赵玉鹏, 赵仁育*：西北师范大学数学与统计学院，甘肃 兰州
关键词: X -GC -投射模；X -GC -投射复形；半对偶模；稳定性；X -GC -Projective Module； X -GC -Projective Complex； Semidualizing Module； Stability
摘要: 设 R 是交换环, C 是一个半对偶 R-模, X 是一个 R-模类. 引入了 X -GC -投射复形的概念, 证明了复形 M 是 X -GC -投射的当且仅当 M 的每个层次上的模都是 X -GC -投射模, 并且对任意的 C-X -复 形 N , M 到 N 的复形态射都是零伦的. 作为应用, 由 X -GC -投射模的性质推得了 X -GC -投射复形的一些性质.
Abstract: Let R be a commutative ring, C a semidualizing R-module and X a class of R-modules. The notion of X-GC-projective complexes is introduced, and it is shown that a complex M is X-GC-projective if and only if each degree of M is X-GC-projective and any morphism from M to N is null homotopic whenever N is a C-X-complex. As applications, some properties of X-GC-projective complexes are deduced from those of X-GC-projective modules.
文章引用：李星宇, 赵玉鹏, 赵仁育. X -GC -投射复形[J]. 理论数学, 2022, 12(10): 1537-1549. https://doi.org/10.12677/PM.2022.1210167

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