论文标题
在豪斯多夫的史坦伯格代数上，较高的半肌素
On Steinberg algebras of Hausdorff ample groupoids over commutative semirings
论文作者
论文摘要
我们研究了由Steinberg引入的Hausdorff ample glassoid的代数。特别是在通勤的半段S上，我们获得了此类Steinberg代数的一致性降低性的完整表征，在S是一个场或通知环时扩展了众所周知的特征。我们还为与任意图相关的图形类固定的Steinberg代数提供了标准，以进行一致性简单。在克拉克（Clark）和模拟人生（Clark and Sims）的结果中，我们表明，在布尔赛（Boolean semifield）上，从莱维特路径代数到斯坦伯格代数的自然同构同构是同构的，并且仅当相关图是行五线时。此外，我们在布尔半场上建立了leavitt路径代数的减少定理和唯一定理。
We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence-simpleness for such Steinberg algebras, extending the well-known characterizations when S is a field or a commutative ring. We also provide a criterion for the Steinberg algebra of the graph groupoid associated to an arbitrary graph to be congruence-simple. Motivated by a result of Clark and Sims, we show that, over the Boolean semifield, the natural homomorphism from the Leavitt path algebra to the Steinberg algebra is an isomorphism if and only if the associated graph is row-finite. Moreover, we establish the Reduction Theorem and Uniqueness Theorems for Leavitt path algebras of row-finite graphs over the Boolean semifield.
