Hereditary atomicity in integral domains

If every subring of an integral domain is atomic, we say that the latter hereditarily atomic. In this paper, study atomic domains. First, characterize when certain direct limits Dedekind domains are in terms overrings. Then use characterization to determine fields On other hand, investigate hereditary atomicity context rings polynomials and Laurent polynomials, characterizing whose respectively, As a result, obtain two classes cannot be embedded into any field. By contrast, show power series never Finally, make some progress on still open question whether satisfies ACCP.