论文标题
$σ$ - 流行戒指及其偏斜的PBW扩展
$Σ$-semicommutative rings and their skew PBW extensions
论文作者
论文摘要
在本文中，我们介绍了$σ$ sepoomumutative ring的概念，以$σ$的一个有限的内态家族$ r $ $ $ $ $。我们将此类的戒指与其他类别的戒指联系起来，例如，减少的Abelian，$σ$ -rigid，nil-cry-cry-cry-cortible和满足$σ$ -Skew反射性nilpotent属性的戒指。此外，我们研究了偏斜pbw扩展的某些环理论特性，超过$σ$ sepoodmutative环。 We prove that if a ring $R$ is $Σ$-semicommutative with certain conditions of compatibility on derivations, then for every skew PBW extension $A$ over $R$, $R$ is Baer if and only if $R$ is quasi-Baer, and equivalently, $A$ is quasi-Baer if and only if $A$ is Baer.最后，我们考虑了超过$σ$ sepormative Cond的偏斜pbw扩展的一些拓扑条件。
In this paper, we introduce the concept of $Σ$-semicommutative ring, for $Σ$ a finite family of endomorphisms of a ring $R$. We relate this class of rings with other classes of rings such that Abelian, reduced, $Σ$-rigid, nil-reversible and rings satisfying the $Σ$-skew reflexive nilpotent property. Also, we study some ring-theoretical properties of skew PBW extensions over $Σ$-semicommutative rings. We prove that if a ring $R$ is $Σ$-semicommutative with certain conditions of compatibility on derivations, then for every skew PBW extension $A$ over $R$, $R$ is Baer if and only if $R$ is quasi-Baer, and equivalently, $A$ is quasi-Baer if and only if $A$ is Baer. Finally, we consider some topological conditions for skew PBW extensions over $Σ$-semicommutative rings.
