关于斜多项式环集外的完全交概念
On the Notion of Complete Intersection outside the Setting of Skew Polynomial Rings
摘要：
在T. Cassidy和作者，完全交的概念定义的（非交换）正则斜多项式环，定义它使用代数和几何工具，其中交换定义是一个特殊情况。在这篇文章中，我们将定义推广到一个更大的代数类，其中包括正则分次斜Clifford代数，量子矩阵的坐标环和泛包络代数的均匀化。正则代数通常被认为是多项式环的非交换模拟，因此本文的结果支持了这一观点。
英文摘要：
In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a special case. In this article, we extend the definition to a larger class of algebras that contains regular graded skew Clifford algebras, the coordinate ring of quantum matrices and homogenizations of universal enveloping algebras. Regular algebras are often considered to be non-commutative analogues of polynomial rings, so the results herein support that viewpoint.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
