On the Notion of Complete Intersection Outside the Setting of Skew Polynomial Rings

Abstract

In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (noncommutative) 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 noncommutative analogues of polynomial rings, so the results herein support that viewpoint.

Key Words:

• Base point
• Clifford algebra
• Complete intersection
• Gorenstein
• Regular algebra
• Skew polynomial ring
• Quadric

2010 Mathematics Subject Classification:

• 14M10
• 16S38
• 16E65

Notes

Communicated by E. Kirkman.