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Proceedings of the American Mathematical Society

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Small regular local Noether lattices. I


Author: Kenneth P. Bogart
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
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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 [Enhancements On Off] (What's this?)

  • [1] Kenneth P. Bogart, Structure theorems for regular local Noether lattices, Michigan Math. J. 15 (1968), 167–176. MR 0227057
  • [2] -, Noether lattices with trivial multiplications, Proc. Amer. Math. Soc. (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0262132-1
Keywords: Noether lattice, local Noether lattice, regular local Noether lattice, Noether lattice imbedding, unique factorization
Article copyright: © Copyright 1970 American Mathematical Society