The equational complexity of Lyndon’s algebra

摘要

The equational complexity of Lyndon’s nonfinitely based 7-element algebra lies between n- 4 and 2n+1. This result is based on a new algebraic proof that Lyndon’s algebra is not finitely based. We prove that Lyndon’s algebra is inherently nonfinitely based relative to a rather rich class of algebras. We also show that the variety generated by Lyndon’s algebra contains subdirectly irreducible algebras of all cardinalities except 0, 1, and 4.