Completion of a Prüfer domain Original Research Article

Let V (resp. D) be a valuation domain (resp. SFT Prüfer domain), I a proper ideal, and image (resp. image) be the I-adic completion of V (resp. D). We show that (1) image is a valuation domain, (2) Krull dimension of image if I is not idempotent, image if I is idempotent, (3) image, (4) image is an SFT Prüfer ring, and (5) image is a catenarian ring.