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- Title
Values of polynomials on centrally closed prime algebras.
- Authors
Lee, Tsiu-Kwen; Lin, Jheng-Huei
- Abstract
Let R be a simple algebra over its extended centroid C , and let f (X 1 , ... , X n) be a noncommutative polynomial having zero constant term. We denote by f (R) + the additive subgroup of R generated by all elements f (x 1 , ... , x n) for x i ∈ R. It is proved that if char R = 0 , then f (R) + is equal to { 0 } , C , [ R , R ] , or R. As to the case char R = p > 0 , an example of a polynomial f satisfying [ R , R ] ⊊ f (R) + ⊊ R is given. Also, the polynomials f with f (R) + = [ R , R ] are characterized if char R = 0 and R ≠ [ R , R ]. Moreover, we work on the context of centrally closed prime algebras to get more general results.
- Subjects
POLYNOMIALS; ALGEBRA; CHAR; CENTROID; COMBUSTION; C*-algebras; POLYNOMIAL rings
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 11, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823502468