On the prime spectrum, Krull dimension and catenarity of integral domains of the form A+XB[[X]]

Let Asubset of or equal toB be integral domains, X an analytic indeterminate over B, and R colon, equals A+XB[[X]]. After determining the height of XB[[X]] in R, we obtain bounds for the (Krull) dimension of R, and determine dim(R) in case B is either a Noetherian or a Prüfer domain containing the quotient field of A. Among our results on catenarity is the following: if B is a Prüfer domain containing the quotient field of A, then R is catenarian if and only if A is catenarian and B is a Dedekind domain. Examples are given to indicate the sharpness of the results.