Coherence and weak factoriality in a certain pullback

Let D be a domain with its quotient field K. Let K[θ]=K[x]/(xn) where x is an indeterminate and θ=x+(xn). Denote by Rn=D+θK[θ], which is a subring of K[θ]. This paper studies several properties of Rn: coherence, weakly factorial rings, strong Mori rings, rings with Noetherian spectrum, weak normality, and t-closedness.