An abstract study of the theory of fractional ideals of a commutative ring is begun. In particular, the definition of principal element in a multiplicative lattice L is used to define a lattice of fractional elements, L*, associated with L. As one application of this definition a theory of Dedekind lattices is developed. This construction also allows the development of an abstract theory of integral closure for a Noether lattice. This theory will be presented in a further paper.
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Richard G. Burton (1975) studied this question.
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