Geodesic
Almost-Dedekind rings
Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 131-134

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout we assume all rings are commutative with identity. We denote the lattice of ideals of a ring R by L(R), and we denote by L(R)* the subposet L(R) − R.A classical result of commutative ring theory is the characterization of a Dedekind domain as an integral domain R in which every element of L(R)* is a product of prime ideals (see Mori [5] for a history). This result has been generalized in a number of ways. In particular, rings which are not necessarily domains but which otherwise satisfy the hypotheses (i.e. general ZPI-rings) have been widely studied (see, for example, Gilmer [3]), as have rings in which only the principal ideals are assumed to satisfy the hypothesis (i.e. π-rings). 
Johnson, E. W. Almost-Dedekind rings. Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 131-134. doi: 10.1017/S0017089500030640
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