S-strong Mori domain of A + XB[X]

Abstract

Let A be an integral domain and S a multiplicative subset of A. We say that A is an S-strong Mori domain (S-SMdomain) if for each nonzero ideal I of A there exist an s \in S and a w-finite type ideal J of I such that sI \subseteq J \subseteq I_w ([10]). Let A \subseteq B be an extension of integral domains, S an anti-Archimedean multiplicative subset of A and X an indeterminate over B. In this note we give, with an additional assumption a necessary and sufficient condition for the polynomial ring A + XB[X] to be an S-SM-domain.

Keywords:  S-strong Mori domains, polynomial rings.

MSC numbers: Primary 13F05; 13E99. Secondary 13A15.

Downloads: Full-text PDF