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- Title
On derivations of differential Ore extensions.
- Authors
Abella, Andrés; Pan, Iván
- Abstract
Let δ : R → R be a derivation of a ring R , and let T = R [ t ; δ ] be the differential Ore extension of R defined by putting t a = a t + δ (a) for all a ∈ R. We describe the derivations of T extending a derivation of R and we deduce an explicit description of every derivation of T in the case where R is the polynomial ring [ x ] over a field . As an application, we compute the first Hochschild cohomology group of [ x ] [ t ; δ ] when δ = x m d / d x and m = 1 , 2 ; for m > 2 a conjectural result is proposed.
- Subjects
POLYNOMIAL rings; ORES
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 3, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824500579