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Join-principal element lattices

Author: E. W. Johnson
Journal: Proc. Amer. Math. Soc. 57 (1976), 202-204
MSC: Primary 06A20
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.

References [Enhancements On Off] (What's this?)

  • [1] E. W. Johnson and J. P. Lediaev, Structure of Noether lattices into join-principal maximal elements, Pacific J. Math. 37 (1971), 101-108. MR 46 #7108. MR 0307993 (46:7108)
  • [2] -, Join-principal elements in Noether lattices, Proc. Amer. Math. Soc. 36 (1972), 73-78. MR 46 #5301. MR 0306174 (46:5301)
  • [3] E. W. Johnson and Michael Detlefson, Prime sequences and distributivity in local Noether lattices, Fund. Math. 86 (1974), 149-156. MR 0414454 (54:2555)

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