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Finiteness properties of differential polynomials

โœ Scribed by Tsiu-Kwen Lee

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
176 KB
Volume
430
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Let R be a prime ring with extended centroid C and let ฯ† X j i be a reduced differential polynomial with coefficients in Q , the symmetric Martindale quotient ring of R, and with zero constant term.

We prove that the finiteness of A ฯ† and the finite-dimensionality of the C-span of A ฯ† are equivalent to that of B ฯ† and that of the C-span of B ฯ† , respectively. Hence some questions on differential polynomials are reduced to those on ordinary generalized polynomials. Let ฮด and d be two derivations of R, L a Lie ideal of R and ฯ a right ideal of R. As applications of our theorems, we obtain the necessary and sufficiency conditions for the finiteness of d(ฯ), d(L) and ฮดd(L) and for the finite-dimensionality of the C-spans of d(ฯ), d(L) and ฮดd(L).

๐Ÿ“œ SIMILAR VOLUMES

On the Finiteness of Certain Rabinowitsc
On the Finiteness of Certain Rabinowitsch Polynomials
โœ Dongho Byeon; H.M. Stark ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 67 KB

Let m be a positive integer and f m (x) be a polynomial of the form f m (x)=x 2 +x -m. We call a polynomial f m (x) a Rabinowitsch polynomial if for t=[ `m] and consecutive integers x=x 0 , x 0 +1, ..., x 0 +t -1, |f(x)| is either 1 or prime. In this note, we show that there are only finitely many R