Going up and Going down relations for Partial Actions on Algebras

In this article, we consider a K − algebra R with a partial action α of a finite group G on it. If each D_g is generated by a central idempotent of R, we answer the question: If P₁ ⊂ P₂ are primes in R and p₂ in R^α with p₂ minimal over P₂ ∩ R^α, does some prime p₁ exist in R^α such that p₁ is minimal over P₁ ∩ R^α and p₁ ⊂ p₂? Similar results are proved by interchanging R and R^α