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TitleThe general PBW property.
Author(s) Huishi Li
TypeArticle in Journal
AbstractFor 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 [24]). 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.

ISSN1005-3867; 0219-1733/e
URL http://www.worldscientific.com/doi/abs/10.1142/S1005386707000508
LanguageEnglish
JournalAlgebra Colloq.
Volume14
Number4
Pages541--554
PublisherWorld Scientific, Singapore; Chinese Academy of Sciences, Academy of Mathematics & Systems Science,
Year2007
Edition0
Translation No
Refereed No
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