Geodesic
Commutative rings with a finite number of indecomposable integral
Izvestiya. Mathematics , Tome 1 (1967) no. 4, pp. 757-772

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The paper answers the question as to the finiteness of the number of nonisomorphic indecomposable integral representations of an arbitrary commutative $Z$-ring. 
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     title = {Commutative rings with a finite number of indecomposable integral},
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Yu. A. Drozd; A. V. Roiter. Commutative rings with a finite number of indecomposable integral. Izvestiya. Mathematics , Tome 1 (1967) no. 4, pp. 757-772. http://geodesic.mathdoc.fr/item/IM2_1967_1_4_a2/