Abstract
A posetX is isomorphic to the poset of all prime ideals of a (distributive) lattice with zero and unit if, and only if,X is the projective limit of an inverse system of finite posets.
Similar content being viewed by others
References
Garrett Birkhoff, Lattice Theory (A.M.S. Colloq. Publ. 25 Providence, R.I) 3rd Edition 1967.
C. C. Chen and G. Grätzer,Stone lattices II: Structure theorems, Can. J. Math.21 (1969), 895–903.
M. Hochster,Prime ideal structure in commutative rings, Trans. Amer. Math. Soc.142 (1969), 43–60.
A. Joyal,Spectral spaces and distributive lattices, Abstract 71T A18 Notices A.M.S.18 (1971), 292.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Speed, T.P. On the order of prime ideals. Algebra Univ. 2, 85–87 (1972). https://doi.org/10.1007/BF02945013
Issue Date:
DOI: https://doi.org/10.1007/BF02945013