χ property in graded skew PBW extensions (2021)
In this paper we study the χ property for algebras which are graded skew PBW extensions. It is shown that if R = ⊕p≥0Rp is a noetherian N-graded algebra and A = σ(R)⟨x1,...,xn⟩ is a graded quasi-commutative skew PBW extension of R, then A satisfies χ if and only if R satisfies χ. Also we give sufficient conditions for that a graded skew PBW extension of R satisfies χ.