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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Join-principal elements in Noether lattices


Authors: E. W. Johnson and J. P. Lediaev
Journal: Proc. Amer. Math. Soc. 36 (1972), 73-78
MSC: Primary 13C05
DOI: https://doi.org/10.1090/S0002-9939-1972-0306174-8
MathSciNet review: 0306174
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Abstract: In this paper we determine the structure of join-principal elements in Noether lattices and we apply these results to obtain the Krull Principal Ideal Theorem for join-principal elements, a representation theorem for a class of Noether lattices, and some interesting ring results.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0306174-8
Keywords: Noether lattice, join-principal element, meet-principal element, principal element, Krull Principal Ideal Theorem, Noetherian ring, general ZPI-ring, Dedekind domain, weak union condition
Article copyright: © Copyright 1972 American Mathematical Society