Vol. 56, No. 1, 1975

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Fractional elements in multiplicative lattices

Richard G. Burton

Vol. 56 (1975), No. 1, 35–49

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.

Mathematical Subject Classification 2000
Primary: 13A15
Secondary: 06A20
Received: 26 October 1973
Published: 1 January 1975
Richard G. Burton