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Azeddine Ouarit (1994) A remark on the
Jacobson property of PI Ore extensions. (Une remarque sur la propriété de Jacobson des extensions de Ore a I.P.) (French) Zbl 0819.16024. Arch. Math. 63, No.2, 136-139 (1994).
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are a class of iterated Ore extensions under suitable constraints that permit to develop a noncommutative extension of the theory of
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Azeddine Ouarit (1992) Extensions de ore d'anneaux noetheriens á i.p, Comm. Algebra, 20 No 6,1819-1837.
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whose properties are relatively well understood. Elements of a Ore extension are called
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328:{\displaystyle \delta (r_{1}r_{2})=\sigma (r_{1})\delta (r_{2})+\delta (r_{1})r_{2}}
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Ore extensions appear in several natural contexts, including skew and differential
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666:, London Mathematical Society Student Texts, vol. 61, Cambridge:
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An
Introduction to Noncommutative Noetherian Rings, Second Edition
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490:= 0 (i.e., is the zero map) then the Ore extension is denoted
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475:{\displaystyle xr=\sigma (r)x+\delta (r)}
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502:) then the Ore extension is denoted
167:{\displaystyle \delta \colon R\to R}
131:{\displaystyle \sigma \colon R\to R}
727:https://zbmath.org/?q=an:0754.16014
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734:https://zbmath.org/?q=an:00687054
698:Graduate Studies in Mathematics
694:Noncommutative Noetherian rings
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522:are Ore extensions, with
47:, is a special type of a
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597:then the Ore extension
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576:principal ideal domain
570:An Ore extension of a
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416:{\displaystyle R}
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16:(Redirected from
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834:Ring theory
790:. Springer.
610:An element
213:satisfying
179:-derivation
100:commutative
45:Øystein Ore
37:ring theory
29:mathematics
770:References
618:is called
593:is a left
572:skew field
558:Properties
90:Definition
641:g·f = f·g
631:R·f = f·R
627:invariant
461:δ
443:σ
387:, is the
368:δ
362:σ
339:Then the
297:δ
275:δ
256:σ
224:δ
193:δ
159:→
153::
150:δ
123:→
117::
114:σ
35:known as
828:Category
804:(1995).
786:(1996).
643:for all
623:twosided
606:Elements
514:Examples
763:0940245
720:1811901
686:2080008
637:central
33:algebra
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494:. If
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174:is a
138:is a
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749:ISBN
706:ISBN
672:ISBN
625:(or
589:and
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518:The
104:ring
647:in
581:If
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486:If
209:of
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27:In
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682:MR
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649:R
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583:σ
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532:σ
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496:σ
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488:δ
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467:r
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278:(
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259:(
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245:2
241:r
235:1
231:r
227:(
183:R
177:σ
162:R
156:R
126:R
120:R
96:R
20:)
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