The General PBW Property
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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.
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2011 ◽
Vol 48
(4)
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pp. 458-474
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2010 ◽
Vol 13
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pp. 111-129
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2015 ◽
Vol 4
(2)
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pp. 1-14
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2018 ◽
Vol 28
(04)
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pp. 553-571
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