Siberian Mathematical Journal

, Volume 46, Issue 2, pp 283–292 | Cite as

Spectra of rings and lattices

  • Yu. L. Ershov


We construct a covariant functor from the category of distributive lattices with bottom and top whose morphisms are bottom and top preserving embeddings to the category of semisimple unital algebras over an arbitrary field whose morphisms are unital embeddings. The spectrum of a distributive lattice is homeomorphic to the spectrum of the ring (algebra) that is its image under this functor.


spectrum of a ring spectrum of a distributive lattice 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hochster M., “Prime ideal structure in commutative rings,” Trans. Amer. Math. Soc., 142, 43–60 (1969).Google Scholar
  2. 2.
    Gierz G., Hofmann K. N., Keimel K., Lawson J. D., Mislove M. W., and Scott D. S., Continuous Lattices and Domains, Cambridge Univ. Press, Cambridge (2003).Google Scholar
  3. 3.
    Hofmann K. H. and Keimel K.. A General Character Theory for Partially Ordered Sets and Lattices, Amer. Math. Soc., Providence RI (1972). (Mem. Amer. Math. Soc.; 122.)Google Scholar
  4. 4.
    Atiyah M. F. and Macdonald I. G., Introduction to Commutative Algebra, Addison-Wesley Publishing Company, Reading etc. (1969).Google Scholar
  5. 5.
    Bourbaki N., Commutative Algebra [Russian translation], Mir, Moscow (1971).Google Scholar
  6. 6.
    Stone M., “Topological representations of distributive lattices and Brouwerian logics,” Časopis Pest. Mat., 67, 1–25 (1937).Google Scholar
  7. 7.
    Grätzer G., General Lattice Theory, Birkhäuser, Basel (1998).Google Scholar
  8. 8.
    Ershov Yu. L., “The spectral theory of semitopological semilattices,” Siberian Math. J., 44, No.5, 797–806 (2003).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Yu. L. Ershov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

Personalised recommendations