nLab
Jonsson-Tarski algebra

Definition

A Jónsson-Tarski algebra is a set AA together with an isomorphism AA×AA\cong A\times A.

Properties

  • Clearly (at least in classical mathematics), any Jónsson-Tarski algebra is either empty, a singleton, or infinite.

  • The structure of a Jónsson-Tarski algebra can be described by an algebraic theory, with one binary operation μ\mu and two unary operations λ\lambda and ρ\rho such that μ(λ(x),ρ(x))=x\mu(\lambda(x),\rho(x)) = x, λ(μ(x,y))=x\lambda(\mu(x,y))=x, and ρ(μ(x,y))=y\rho(\mu(x,y))=y.

  • The category of Jónsson-Tarski algebras is a topos, although this is not in general the case for algebraic theories. See here.

Revised on March 2, 2014 15:43:53 by Tim Campion? (173.76.91.172)