Idempotent generated algebras and Boolean powers of commutative rings

4 pages•Published: July 28, 2014

Guram Bezhanishvili, Vincenzo Marra, Patrick J. Morandi and Bruce Olberding

Abstract

For a commutative ring R, we introduce the notion of a Specker R-algebra and show that Specker R-algebras are Boolean powers of R. For an indecomposable ring R, this yields an equivalence between the category of Specker R-algebras and the category of Boolean algebras. Together with Stone duality this produces a dual equivalence between the category of Specker R-algebras and the category of Stone spaces.

Keyphrases: boolean power, compact hausdorff space, specker algebra

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 31-34.

Links:	https://easychair.org/publications/paper/qP
	https://doi.org/10.29007/dgb4

BibTeX entry

@inproceedings{TACL2013:Idempotent_generated_algebras_Boolean,
  author    = {Guram Bezhanishvili and Vincenzo Marra and Patrick J. Morandi and Bruce Olberding},
  title     = {Idempotent generated algebras and Boolean powers of commutative rings},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/qP},
  doi       = {10.29007/dgb4},
  pages     = {31-34},
  year      = {2014}}

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