Symmetric Utumi quotient rings of Ore extensions by skew derivations

Chuang, Chen-Lian; Tsai, Yuan-Tsung

doi:10.1090/s0002-9939-10-10342-6

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Cited by 2 publications

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“…The condition (3) comes in because the Hopf algebra in the context of Ore extension R X D is a smash product of R with k X , the free k-algebra considered as the universal enveloping algebra of the free Lie k-algebra X generated by X ( [7,8]). We refer the details to [5,6,8]. Each of the three conditions (1), (2), and (3) does not seem easy to verify for a particular application.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Martindale Quotient Rings of Ore Extensions with More than One Indeterminate

Chuang

Tsai

2015

Communications in Algebra

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Let R be a domain and D a sequence of derivations of R with length ≥ 2. Let Q D s R be the subring consisting of those q in the symmetric Martindale quotient ring of R such that qI ∪ Iq ⊆ R for a nonzero D-invariant ideal I of R. It is shown here that the symmetric Martindale quotient ring of the Ore extension R X D is the Ore extension Q D s R X D . Our proof depends on an interesting combinatoric result on words.

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