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Spectra of rings and lattices

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Abstract

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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk

    Yu. L. Ershov

Authors
  1. Yu. L. Ershov
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Additional information

The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2069.2003.1).

Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Zhurnal, Vol. 46, No. 2, pp. 361–373, March–April, 2005.

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Ershov, Y.L. Spectra of rings and lattices. Sib Math J 46, 283–292 (2005). https://doi.org/10.1007/s11202-005-0029-7

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  • DOI: https://doi.org/10.1007/s11202-005-0029-7

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