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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Small regular local Noether lattices. I
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by Kenneth P. Bogart
Proc. Amer. Math. Soc. 25 (1970), 423-428
DOI: https://doi.org/10.1090/S0002-9939-1970-0262132-1
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Abstract:

In a recent paper the author has discussed the structure of regular local Noether lattices. In this paper it is proved that if a regular local Noether lattice has precisely $3$ minimal primes, then it is isomorphic to $R{L_3}$, the lattice of the lattice of ideals of $F[{x_1},{x_2},{x_3}]$ generated by the principal ideals $({x_1}),({x_2})$ and $({x_3})$ under join and multiplication.
References
  • Kenneth P. Bogart, Structure theorems for regular local Noether lattices, Michigan Math. J. 15 (1968), 167–176. MR 227057
    • —, Noether lattices with trivial multiplications, Proc. Amer. Math. Soc. (to appear).
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 423-428
  • MSC: Primary 06.70
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0262132-1
  • MathSciNet review: 0262132