Poisson Dixmier-Moeglin equivalence from a topological point of view

A complex affine Poisson algebra is said to satisfy the Dixmier-Moeglin equivalence if cores of maximal ideals are precisely those prime that locally closed in spectrum P.spec and if, moreover, these whose extended centers exactly numbers. In this paper, we provide some topological criteria for terms poset (P.spec A, ⊆) symplectic leaf or core stratification on its spectrum. particular, prove Zariski topology each can detect any algebra. Moreover, generalize weaker version a proved [J. Bell, S. Launois, O. L. Sanchez B. Moosa, algebras via model theory differential-algebraic geometry, J. Eur. Math. Soc. (JEMS) 19 (2017), 2019–2049] general context commutative differential