Open AccessIdempotent generated algebras and Boolean powers of commutative rings
Author(s) -
Guram Bezhanishvili,
Vincenzo Marra,
Patrick J. Morandi,
Bruce Olberding
Publication year - 2018
Publication title -
epic series in computing
Language(s) - English
Resource type - Conference proceedings
ISSN - 2398-7340
DOI - 10.29007/dgb4
Subject(s) - mathematics , stone's representation theorem for boolean algebras , indecomposable module , idempotence , boolean ring , boolean algebras canonically defined , equivalence (formal languages) , pure mathematics , commutative property , complete boolean algebra , duality (order theory) , dual (grammatical number) , ring (chemistry) , commutative ring , free boolean algebra , two element boolean algebra , algebra over a field , algebra representation , principal ideal ring , art , chemistry , literature , organic chemistry
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.