%0 Journal Article
%T 相对于余挠对的Gorenstein投射表示<br> Gorenstein Projective Representations Relative to Cotorsion Pairs
%A 连许贤
%J Pure Mathematics
%P 221-231
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/PM.2025.155171
%X 设 Q 是一个有限无圈箭图,R是一个环,Rep(Q,R)是 Q 的左 R- 模表示范畴。本文描述了 Rep(Q,R) 中相对于余挠对的 Gorenstein 投射表示。具体地，我们证明了X∈Rep(Q,R) 是相对于(A,B)的 Gorenstein 投射表示当且仅当对任意的i∈？？<sub>0</sub>,<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">
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</math>是单同态,并且X(i),Cokerφ<sub>i</sub><sup style=\"margin-left:-6px;\">X</sup>是相对于 (A,B)的Gorenstein投射模.<br>Let Q be a finite acyclic quiver, R a ring, and Rep(Q,R) the category of left  R-module representations of Q. This paper characterizes Gorenstein projective representations in Rep(Q, R) relative to cotorsion pairs. Specifically, we prove that a representation X∈Rep(Q, R) is Gorenstein projective relative to (A, B) if and only if} for every vertex i∈Q<sub>0</sub>, the canonical morphism <math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">
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%K 箭图，余挠对，相对于余挠对的Gorenstein投射表示<br>Quiver
%K Cotorsion Pairs
%K Gorenstein Projective Representations with Respect to Cotorsion Pairs
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=115870