A ternary self-distributive algebra is an algebra $(X,t)$ that satisfies the identity $$t(u,v,t(x,y,z))=t(t(u,v,x),t(u,v,y),t(u,v,z)).$$ Is the variety of ternary self-distributive algebras generated by a set of finite algebras? Under the existence of a rank-into-rank cardinal, I have proven that the variety of binary self-distributive algebras is generated by its finite algebras. For the ternary case, I do not have much intuition about the situation.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.