发表机构
Lanzhou University of Technology（兰州理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究\(T -\)模堆范畴中投射对象和戈伦斯坦投射对象定义，证明相关充要条件，给出BP戈伦斯坦投射维数的函子描述，还证明单位桁架\(T\)是戈伦斯坦桁架的充要条件是\(R(T)\)是岩泽 - 戈伦斯坦环。
AI 中文摘要
本文给出了\(T -\)模堆范畴中投射对象和戈伦斯坦投射对象的定义，其中\(T\)是一个桁架。证明了\(T -\)模堆\(P\)是投射的当且仅当对于所有\(e_p\in P\)，\(\mathcal{G}_{e_p}(P)\)是投射\(R(T)\) - 模；\(T -\)模堆\(M\)是BP戈伦斯坦投射的当且仅当对于所有\(e_m\in M\)，\(\mathcal{G}_{e_m}(M)\)是戈伦斯坦投射\(R(T)\) - 模。还给出了BP戈伦斯坦投射维数的函子描述。最后证明了单位桁架\(T\)是戈伦斯坦桁架当且仅当\(R(T)\)是岩泽 - 戈伦斯坦环。
英文摘要
The definitions of projective objects and Gorenstein projective objects in the category of heaps of $T$-modules are posed, where $T$ is a truss. It is shown that a heap of $T$-modules $P$ is projective if and only if $\mathcal{G}_{e_p}(P)$ is a projective $R(T)$-module for all $e_p\in P$ and a heap of $T$-modules $M$ is BP Gorenstein projective if and only if $\mathcal{G}_{e_m}(M)$ is a Gorenstein projective $R(T)$-module for all $e_m\in M$. Moreover, we give a functorial description of the BP Gorenstein projective dimension. Finally, it is also proven that a unital truss $T$ is a Gorenstein truss if and only if $R(T)$ is an Iwanaga-Gorenstein ring.
CommentsWe have updated Section 5
