论文标题
雅各布森代数$ k <x，y |上的注射模块xy = 1> $
Injective modules over the Jacobson algebra $K< X,Y | XY = 1 >$
论文作者
论文摘要
对于字段$ k $，令$ \ m varycal {r} $表示jacobson代数$ k \ langle x，y \ | \ xy = 1 \ rangle $。我们为（无限多）简单的$ \ MATHCAL {R} $模块的每个（无限多）简单的Injembelope进行了明确的构造。因此，我们获得了$ \ Mathcal {r} $的最小注射式Cogenerator的明确描述。我们的方法涉及实现$ \ MATHCAL {R} $以同构为同构，作为适当的图形$ \ Mathcal {T} $的Leavitt Path $ K $ -Algebra，从而使我们能够利用为该类别的代数为代数开发的重要机械。
For a field $K$, let $\mathcal{R}$ denote the Jacobson algebra $K\langle X, Y \ | \ XY=1\rangle$. We give an explicit construction of the injective envelope of each of the (infinitely many) simple left $\mathcal{R}$-modules. Consequently, we obtain an explicit description of a minimal injective cogenerator for $\mathcal{R}$. Our approach involves realizing $\mathcal{R}$ up to isomorphism as the Leavitt path $K$-algebra of an appropriate graph $\mathcal{T}$, which thereby allows us to utilize important machinery developed for that class of algebras.
