2016/07/14 by Jason P. Bell, Bell, Jason, Kaiyu Wu +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1607.04131
openalex publication_date 2016/07/14 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28
An algebra A satisfies the Dixmier-Moeglin equivalence if we have the equivalences: P~\rm primitive\iff P~\rm rational\iff P ~\rm locally~closed~ ~\rm for~P∈ \rm Spec(A). We study the robustness of the Dixmier-Moeglin equivalence under extension of scalars and under the formation of Ore extensions. In particular, we show that the Dixmier-Moeglin equivalence is preserved under base change for finitely generated complex noetherian algebras. We also study Ore extensions of finitely generated complex noetherian algebras A. If T:A→ A is either a ℂ-algebra automorphism or a ℂ-linear derivation of A, we say that T is frame-preserving if there exists a finite-dimensional subspace V⊆ A that generates A as an algebra such that T(V)⊆ V. We show that if A is of finite Gelfand-Kirillov dimension and has the property that all prime ideals of A are completely prime and A satisfies the Dixmier-Moeglin equivalence then the Ore extension A[x;T] satisfies the Dixmier-Moeglin equivalence whenever T is a frame-preserving derivation or automorphism.