Geodesic
A Structural Approach to Noether Lattices
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 657-665

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we explore the extent to which embedding and isomorphism questions about a Noether lattice L can be reduced to questions about simpler structures associated with L.In § 1, we use a variation of Dilworth's congruence approach [2] to associate a collection of semi-local Noether lattices with a given Noether lattice L. We show that these semi-localizations determine L to within isomorphism (Corollary 1.5); thus embedding and isomorphism questions about L are largely reduced to the semi-local case.In § 2, we consider the influence on a semi-local Noether lattice L of the substructure ∂ L consisting of all elements, all of whose associated primes are maximal. Here we find that if ∂ L can be embedded in a semi-local Noether lattice L *, then L can be embedded in an extension of L *. 
Johnson, E. W.; Johnson, J. A.; Lediaev, J. P. A Structural Approach to Noether Lattices. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 657-665. doi: 10.4153/CJM-1970-072-9
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