Boolean sets, skew Boolean algebras and a non-commutative Stone duality

Ganna Kudryavtseva; Mark Lawson

doi:10.1007/s00012-015-0361-0

Boolean sets, skew Boolean algebras and a non-commutative Stone duality

Ganna Kudryavtseva
, Mark Lawson^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

109 Downloads (Pure)

Abstract

We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets and étalé spaces over Boolean spaces.

Original language	English
Pages (from-to)	1-19
Number of pages	19
Journal	Algebra Universalis
Volume	75
Issue number	1
Early online date	7 Dec 2015
DOIs	https://doi.org/10.1007/s00012-015-0361-0
Publication status	Published - Feb 2016

ASJC Scopus subject areas

Algebra and Number Theory

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title = "Boolean sets, skew Boolean algebras and a non-commutative Stone duality",

abstract = "We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets and {\'e}tal{\'e} spaces over Boolean spaces.",

author = "Ganna Kudryavtseva and Mark Lawson",

note = "{"}The first author was partially supported by ARRS grant P1-0288, and the second by EPSRC grant EP/I033203/1.{"}",

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N2 - We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets and étalé spaces over Boolean spaces.

AB - We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets and étalé spaces over Boolean spaces.

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DO - 10.1007/s00012-015-0361-0

M3 - Article

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SP - 1

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JO - Algebra Universalis

JF - Algebra Universalis

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Boolean sets, skew Boolean algebras and a non-commutative Stone duality

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