发表机构
University of Colorado, Colorado Springs; Università degli Studi di Verona; Università degli Studi di Padova（科罗拉多大学科泉分校; 维罗纳大学; 帕多瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对Leavitt路代数上由排他圈产生的单模，构造无穷级数K-向量空间上的模结构，给出其内射包络的显式刻画，将相关结果推广至所有有限或无限图及所有排他圈。
AI 中文摘要
设K为任意域，E为任意有向图，L_K(E)为对应的Leavitt路代数。如Chen最初描述、后被Ara与Rangaswamy推广的结论，对E中的每个圈c，可构造单左L_K(E)-模V_c^E，更一般地可构造V_{p(x),c}^E（其中p(x)为K[x,x^{-1}]中的不可约多项式）。若圈c的所有顶点都不支撑除c自身外的其他圈，则称c是排他圈。本文主要结果为，对每个排他圈c，给出V_c^E乃至更一般的V_{p(x),c}^E的内射包络的显式刻画。所用方法是在适当构造的无穷级数K-向量空间上定义L_K(E)-模结构。该结果显著推广了作者此前的工作，适用范围覆盖所有图（有限或无限）及所有排他圈。
英文摘要
Let $K$ be any field, $E$ any directed graph, and $L_K(E)$ the associated Leavitt path algebra. As described first by Chen, and subsequently generalized by Ara and Rangaswamy, for each cycle $c$ in $E$ one can build the simple left $L_K(E)$-module $V_c^E$, and then more generally $V_{p(x),c}^E$ (where $p(x)$ is an irreducible polynomial in $K[x,x^{-1}]$). A cycle $c$ is called {\it exclusive} in case none of the vertices of $c$ is the base of any cycle other than $c$. In our main result we provide an explicit description of the injective envelope of $V_c^E$, and then more generally of $V_{p(x),c}^E$, for each exclusive cycle $c$. Our method involves defining an $L_K(E)$-module structure on an appropriately-built $K$-vector space of infinite series. Our main result significantly generalizes previous work of the authors, in that the result holds for all graphs (finite or not), and all exclusive cycles.
