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Proceedings of the American Mathematical Society

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

 
 

 

Join-principal element lattices


Author: E. W. Johnson
Journal: Proc. Amer. Math. Soc. 57 (1976), 202-204
MSC: Primary 06A20
DOI: https://doi.org/10.1090/S0002-9939-1976-0404067-2
MathSciNet review: 0404067
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Abstract: Let $ (\mathfrak{L},M)$ be a local Noether lattice. If the maximal element $ M$ is meet principal, it is well known and easily seen that every element of $ \mathfrak{L}$ is meet principal. In this note, we obtain the corresponding result for $ M$ join-principal. We also consider join-principal elements generally under the assumption of the weak union condition and show, for example, that the square of a join-principal element is principal.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0404067-2
Article copyright: © Copyright 1976 American Mathematical Society

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