The General PBW Property

• 来源期刊: 代数集刊（英文版）
• 关键词: PBW property graded algebra Gr(o)bner basis
• 年，卷（期）: 2007,（4）
• 页码范围: 541-554
• 页数: 14页
• 语种: 英文

摘要

For ungraded quotients of an arbitrary Z-graded ring, we define the general PBW property, that covers the classical PBW property and the N-type PBW property studied via the N-Koszulity by several authors (see [2-4]). In view of the noncommutative Gr(o)bner basis theory, we conclude that every ungraded quotient of a path algebra (or a free algebra) has the general PBW property. We remark that an earlier result of Golod [5]concerning Gr(o)bner bases can be used to give a homological characterization of the general PBW property in terms of Shafarevich complex. Examples of applicatipn are given.