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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- 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).
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06.70
Retrieve articles in all journals with MSC: 06.70
Additional Information
Keywords:
Noether lattice,
local Noether lattice,
regular local Noether lattice,
Noether lattice imbedding,
unique factorization
Article copyright:
© Copyright 1970
American Mathematical Society