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Boletín de la Sociedad Matemática Mexicana

, Volume 25, Issue 3, pp 687–700 | Cite as

Nearly spectral spaces

  • Lorenzo Acosta
  • Ibeth Marcela Rubio PerillaEmail author
Original Article
  • 36 Downloads

Abstract

We study some natural generalizations of spectral spaces in the contexts of commutative rings and distributive lattices. We obtain a topological characterization for the spectra of commutative (not necessarily unitary) rings and we find spectral versions for the up-spectral and down-spectral spaces. We show that the duality between distributive lattices and Balbes–Dwinger spaces is the co-equivalence associated with a pair of contravariant right adjoint functors between suitable categories.

Keywords

Spectral space Down-spectral space Up-spectral space Stone duality Prime spectrum Distributive lattice Commutative ring 

Mathematics Subject Classification

54H10 54F65 54D35 

Notes

Acknowledgements

We want to thank the referees for their useful comments.

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Copyright information

© Sociedad Matemática Mexicana 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversidad Nacional de ColombiaBogotáColombia

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