Some classification of certain integral domains via conductor overrings and semistar operations

Abstract

Among other results, given an integral domain R, we show that if coincides the set of valuation overrings of R, then, R must be an almost pseudo-valuation domain in the sense of Badawi and Houston [8]. Using this, we classify certain classes of totally divisorial conducive domains. The proof that an integrally closed conducive domain that has an m-canonical ideal is a valuation domain is also given, providing a partial answer to the questions raised by Heinzer et al. [33].