an:06296564
Zbl 1372.16025
Jordan, David A.
Ore extensions and Poisson algebras
EN
Glasg. Math. J. 56, No. 2, 355-368 (2014).
00332637
2014
j
16S36 13N15 17B63
derivation of commutative Noetherian \(\mathbb C\)-algebra; homeomorphism; prime spectrum of Ore extension; Poisson prime spectrum of polynomial algebra
Summary: For a derivation \(\delta\) of a commutative Noetherian \(\mathbb C\)-algebra \(A\), a homeomorphism is established between the prime spectrum of the Ore extension \(A[z;\delta]\) and the Poisson prime spectrum of the polynomial algebra \(A[z]\) endowed with the Poisson bracket such that \(\{A,A\}=0\) and \(\{z,a\}=\delta(a)\) for all \(a \in A\).