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].
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