关于标准等值的一点注记

A note on singular equivalences and idempotents

Let $Λ$ be an Artin algebra and let $e$ be an idempotent in $Λ$. We study certain functors which preserve the singularity categories. Suppose $\mathrm{pd}Λe_{eΛe}<\infty$ and $\mathrm{id}_Λ\tfrac{Λ/\langle e\rangle}{\mathrm{rad}Λ/\langle e\rangle} < \infty$, we show that there is a singular equivalence between $eΛe$ and $Λ$.

A note on the Diximier-Mouglin Equivalence in Leavitt path algebras of arbitrary graphs over a field

The Dixmier-Moeglin Equivalence (for short, the DM-equivalence) is the equivalence of three distinguishing properties of prime ideals in a non-commutative algebra A. These properties are of (i) being primitive, (ii) being rational, and (iii) being locally closed in the Zariski topology of Spec(A). The DM-equivalence holds in many interesting algebras over a field. Recently, it was shown that the prime ideals of a Leavitt path algebra of a finite graph satisfy the DM-equivalence, In this note, we investigate the occurrence of the DM-equivalence in a Leavitt path algebra L of an arbitrary direct…

关于Ariki-Koike代数范畴作用的范围等价注记

A Note on Scopes Equivalences for Ariki--Koike Algebras as Categorical Actions

本文探讨了Ariki-Koike代数中范畴作用的范围等价转换方法，通过抽象结果与具体应用的结合，揭示了权重空间的Morita等价类划分。

关于与图逆半群Morita等价的注记

A note on Morita equivalence to graph inverse semigroups

该研究刻画了与图逆半群Morita等价的逆半群，并将相关结论推广到与左可消范畴关联的逆半群情形。

关于环扩展中莫里塔等价的注记

Note on Morita equivalence in ring extensions

本文研究环扩展中莫里塔等价的性质，证明若干扩展类别的莫里塔不变性，并给出非莫里塔不变的环扩展类别的例子。

导离散代数与标准等价

The derived-discrete algebras and standard equivalences

我们证明了有限整体维数的导离散代数之间的任何导等价都是标准的，即通过双侧倾斜复形同构于导张量函子。