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Dergiler / International Electronic Journal of Algebra / 2014 / Cilt: 15 - Sayı: 15

CENTRALIZERS IN ORE EXTENSIONS OF POLYNOMIAL RINGS

Johan RİCHTER
Sergei SİLVESTROV
Sayfa
196–207
Yayın Tarihi
2014-06-01
DOI
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We also show that for certain classes of elements their centralizer is singly generated as an algebra.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we consider centralizers of single elements in certain Ore extensions, with a non-invertible endomorphism, of the ring of polynomials in one variable over a field.
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Temel Bulgular & Veri:We show that they are commutative and finitely generated as algebras.
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Sonuç & Katkı:We also show that for certain classes of elements their centralizer is singly generated as an algebra.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ore extension · centralizer

Abstract

In this paper, we consider centralizers of single elements in certain Ore extensions, with a non-invertible endomorphism, of the ring of polynomials in one variable over a field. We show that they are commutative and finitely generated as algebras. We also show that for certain classes of elements their centralizer is singly generated as an algebra.

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Bu Makaleye Atıf Yap

RİCHTER, J., SİLVESTROV, S. (2014). CENTRALIZERS IN ORE EXTENSIONS OF POLYNOMIAL RINGS. International Electronic Journal of Algebra, Cilt: 15 - Sayı: 15, 196–207. https://ajindex.com/articles/832432

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Kaynakça (7)

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  7. L. Makar-Limanov, Centralizers in the quantum plane algebra, Studies in Lie theory, Progr. Math., vol. 243, Birkh¨auser Boston, Boston, MA, 2006, pp. 411– J. Richter, Burchnall-Chaundy theory for Ore extensions, Proceedings of the AGMP, Springer-Verlag, (to appear). X. Tang, Maximal commutative subalgebras of certain skew polynomial rings, Johan Richter Centre for Mathematical Sciences Lund University Box 118, SE-22199 Lund, Sweden e-mail: [email protected] Sergei Silvestrov Division of Applied Mathematics The School of Education, Culture and Communication M¨alardalen University Box 883, SE-72123 V¨aster˚as, Sweden e-mail: [email protected]