On the Finiteness of Gröbner Bases Computation in Quotients of the Free Algebra

2001 ◽  
Vol 11 (3) ◽  
pp. 157-180 ◽  
Author(s):  
Patrik Nordbeck
Keyword(s):  
Free Algebra ◽  
Gröbner Bases ◽  
Grobner Bases

The General PBW Property

2007 ◽  
Vol 14 (04) ◽  
pp. 541-554
Author(s):  
Huishi Li
Keyword(s):  
Free Algebra ◽  
Gröbner Basis ◽  
Gröbner Bases ◽  
Path Algebra ◽  
Grobner Bases ◽  
Grobner Basis ◽  
Graded Ring ◽  
Homological Characterization

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.

scholarly journals Gröbner bases for operads

2010 ◽  
Vol 153 (2) ◽  
pp. 363-396 ◽  
Author(s):  
Vladimir Dotsenko ◽  
Anton Khoroshkin
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases

scholarly journals Gröbner bases over fields with valuations

2018 ◽  
Vol 88 (315) ◽  
pp. 467-483 ◽  
Author(s):  
Andrew J. Chan ◽  
Diane Maclagan
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases
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