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The notion of isomorphism of stable AF-C*-algebras is considered in thispaper in the case when the corresponding Bratteli diagram is stationary, i.e.,is associated with a single square primitive nonsingular incidence matrix.C*-isomorphism induces an equivalence relation on these matrices, calledC*-equivalence. We show that the associated isomorphism equivalence problem isdecidable, i.e., there is an algorithm that can be used to check in a finitenumber of steps whether two given primitive nonsingular matrices areC*-equivalent or not.Comment: 55 pages, LaTeX2e (amsart class). In this version the main theorem  has been extended to possibly singular primitive integer matrixes, and the  clarity of the presentation has been improved substantially throughout the  pape

Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups