Semiprime factorizations in unions of Dedekind domains.

Throughout this section D will denote an almost Dedekind domain with quotient field K. This means that, for every maximal ideal P of D, the quotient ring DP is a Dedekind domain (and hence a rank-one discrete valuation ring). Almost Dedekind domains are examined in [1] — [12]. A semiprime ideal of D is equal to its radical. A maximal ideal P of D is called critical if every finite subset of P is contained in the square of a maximal ideal of D. Critical ideals are discussed in [1].