On the Krull and valuative dimension of \(D+XD_ S[X]\) domains
This paper is concerned with the integral domain \(D^{(S,r)}=D+(X_ 1,X_ 2,...,X_ r)D_ S[X_ 1,...,X_ r]\), where D is an integral domain and S is a multiplicative subset of D. \textit{Costa}, \textit{Mott} and \textit{Zafrullah} considered the prime ideal structure of such domains where \(r=1\). The authors extend that work to \(n>1\). In particular they determine when \(D^{(S,r)}\) is a strong S-domain, a stably strong S- domain, a catenarian domain and a universally catenarian domain. As a consequence, they obtain a new class of non-Noetherian universally catenarian domains. Further, they provide an explicit formula for the Krull dimension of \(D^{(S,r)}\).
scientific article; zbMATH DE number 4144102
scientific article