PACKAGE DEAL THEOREMS AND SPLITTING ORDERS IN DIMENSION-1

Let Lambda be a module-finite algebra over a commutative noetherian ri ng R of Krull dimension 1. We determine when a collection of finitely generated modules over the localizations Lambda(m), at maximal ideals of R, is the family of all localizations M(m) of a finitely generated Lambda-module M. When R is semilocal we also determine which finitely generated modules over the J(R)-adic completion of Lambda are completi ons of finitely generated A-modules. If Lambda is an R-order in a semi simple artinian ring, but not contained in a maximal such order, sever al of the basic tools of integral representation theory behave differe ntly than in the classical situation. The theme of this paper is to de velop ways of dealing with this, as in the case of localizations and c ompletions mentioned above. In addition, we introduce a type of order called a ''splitting order'' of Lambda that can replace maximal orders in many situations in which maximal orders do not exist.