The equational complexity of Lyndon’s algebra

Algebra universalis（2011）

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摘要

The equational complexity of Lyndon’s nonfinitely based 7-element algebra lies between n − 4 and 2 n + 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.

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关键词

Equational complexity,variety of algebras,relatively inherently nonfinitely based,shift automorphism method,Lyndon’s algebra,automatic algebra,finite algebra membership problem

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