论文标题
eTale gropoid代数的链条件
Chain Conditions for Etale Groupoid Algebras
论文作者
论文摘要
让$ r $成为带有单位的Unitual“交换戒指”和$ \ Mathscr {g} $ a ample groupoid。使用groupoid $ \ mathscr {g} $的拓扑，Steinberg定义了etale groupoid代数$ r \ Mathscr {g} $。这些eTale groupoid代数概括了各种代数，包括基团代数，交换代数在由基于IDEMPOTENTS产生的磁场上，传统的Groupoid代数，Leavitt Path代数，更高秩代数代数，较高级别图代数和逆半群代数。 Steinberg后来表征了Etale groupoid代数的经典链条件。我们从类似地表征了Noetherian和Artinian，本地Noetherian和Artinian，以及半神经eTale groupoid代数，从而概括了Leavitt Path代数的现有结果。
Let $R$ be a unital commutative ring with unit and $\mathscr{G}$ an ample groupoid. Using the topology of the groupoid $\mathscr{G}$, Steinberg defined an etale groupoid algebra $R\mathscr{G}$. These etale groupoid algebras generalize various algebras including group algebras, commutative algebras over a field generated by idempotents, traditional groupoid algebras, Leavitt path algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg later characterized the classical chain conditions for etale groupoid algebras. We characterize categorically noetherian and artinian, locally noetherian and artinian, and semisimple etale groupoid algebras, generalizing existing results for Leavitt path algebras.
