Derivations with algebraic values of bounded degree
Resource
Communications in Algebra 27 (4): 1911-1920
Journal
Communications in Algebra
Pages
1911-1920
Date Issued
1999
Date
1999
Author(s)
Lee, T.-K.
Lee, T. C.
Abstract
Let R be a prime algebra over a field F, d a nonzero derivation of R and ρ a nonzero right ideal of R. Suppose that for every cursive Greek chi ∈ ρ, d(cursive Greek chi) is algebraic over F of bounded degree. Then R is a primitive ring with a minimal right ideal eR, where e = e2 ∈ R and eRe is a finite-dimensional central division algebra, except when d is an inner derivation induced by an element a in the two-sided Martindale quotient ring of R such that aρ = 0. An analogous result is also proved for the Lie ideal case.
Type
journal article
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