Examples, Counterexamples, and Structure in Bounded Width Algebras
نویسنده
چکیده
We study bounded width algebras which are minimal in the sense that every proper reduct does not have bounded width. We show that minimal bounded width algebras can be arranged into a pseudovariety with one basic ternary operation. We classify minimal bounded width algebras which have size at most three, and prove a structure theorem for minimal bounded width algebras which have no majority subalgebra, which form a pseudovariety with a commutative binary operation. We provide a counterexample to a recent conjecture about three variable Mal’cev conditions for bounded width algebras, and we show that any two variable Mal’cev condition which holds in the two element semilattice and majority algebras holds in every bounded width algebra.
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