1. The General PBW Property.
- Author
-
Huishi Li
- Subjects
- *
RING theory , *MATHEMATICAL analysis , *MATHEMATICS education , *LINEAR algebra , *BASES (Linear topological spaces) - Abstract
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 Gröbner 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 Gröbner bases can be used to give a homological characterization of the general PBW property in terms of Shafarevich complex. Examples of application are given. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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