论文标题
LEAVITTT路径代数的分级结构被视为部分偏斜组环
The graded structure of Leavittt path algebras viewed as partial skew group rings
论文作者
论文摘要
令$ e $为有向图，$ \ mathbb k $是一个字段，$ \ mathbb f $是$ e $边缘的免费组。在这项工作中，我们将Leavitt Path代数与部分偏斜组环之间的同构赋予$ L _ {\ Mathbb K}（E）$的$ \ Mathbb f $ - 分类，并研究该分级的一些代数属性。更确切地说，我们表明划分清洁度，分级单位定型性和$ l _ {\ Mathbb k}（e）$的强度等级都是等效的。
Let $E$ be a directed graph, $\mathbb K$ be a field, and $\mathbb F$ be the free group on the edges of $E$. In this work, we use the isomorphism between Leavitt path algebras and partial skew group rings to endow $L_{\mathbb K}(E)$ with an $\mathbb F$-gradation and study some algebraic properties of this gradation. More precisely, we show that graded cleanness, graded unit-regularity, and strong gradeness of $L_{\mathbb K}(E)$ are all equivalent.
