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| Titel: |
Discrete Valuations Extend to Certain Algebras of Quantum Type |
| Auteur: |
Moawad, Hussein Van Oystaeyen, Freddy |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 24 (1996) nr. 8 pagina's 2551-2566 |
| Jaar: |
1996 |
| Inhoud: |
So-called “quantized” algebras are popular objects of study in non-commutative algebra. Usually such algebras are either positively graded Ore domains R with R0 = K a field and R = K[R1], R1 being a finite dimensional K vectorspace, or else filtered rings having a ring of forementioned type for its associated graded ring. We show that every discrete valuation of K extends to a valuation, in the sence of O. Schilling (cf. [S]), of the skewfield of fractions, Δ = Qcl(R), of the Ore domain R (Proposition 2.3. and Corollary 2.8.). Such extension property has long been known to fail for finite dimensional skewfields over K; its validity in the case of several quantized algebras may be viewed as a consequence of the rigidity of their defining relations. Our result opens the door for a more arithmetical study of Δ e.g. in case K is a numberfield or an algebraic function field of a curve; for an application in this direction we refer to a first version of some divisor calculus started in [VW]. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 4 van 13 gevonden artikelen
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