Idempotent generated algebras and Boolean powers of commutative rings | Zendy

Guram Bezhanishvili | Zendy; Vincenzo Marra | Zendy; Patrick J. Morandi | Zendy; Bruce Olberding | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Idempotent 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 , equivalence (formal languages) , boolean ring , pure mathematics , boolean algebras canonically defined , commutative property , complete boolean algebra , duality (order theory) , ring (chemistry) , dual (grammatical number) , commutative ring , interior algebra , two element boolean algebra , algebra over a field , non associative algebra , 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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research