Geodesic
Noether Lattices Representable as Quotients of the Lattice of Monomially Generated Ideals of Polynomial Rings
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 789-799

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Noether lattices were introduced by R. P. Dilworth in [5] and constitute a natural abstraction of the lattice of ideals of a Noetherian ring. In his definitive work, Dilworth showed that a minimal prime of an element generated by n principal elements has rank ≦ n. Following standard ring theoretical terminology, a local Noether lattice with (unique) maximal element M is said to be regular if M has rank n and can be generated by n principal elements.In [3], K. P. Bogart showed that a distributive regular local Noether lattice of Krull dimension n is isomorphic to RLn, the sublattice of all ideals generated by monomials of any polynomial ring (k a field). In a later paper [4], Bogart extended his results on distributive regular local Noether lattices by showing that any distributive local Noether lattice is the image of a multiplicative map θ which preserves joins, and can in fact be thought of as the related congruence lattice. 
Anderson, D. D.; Johnson, E. W.; Johnson, J. A. Noether Lattices Representable as Quotients of the Lattice of Monomially Generated Ideals of Polynomial Rings. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 789-799. doi: 10.4153/CJM-1979-072-8
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