Lee monoid L₄¹ is non-finitely based

2017/10/01 by Mikhailova, Inna, Sapir, Olga
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1710.00820

Abstract

We establish a new sufficient condition under which a monoid is non-finitely based and apply this condition to show that the 9-element monoid L₄¹ is non-finitely based. The monoid L₄¹ was the only unsolved case in the finite basis problem for Lee monoids L_ℓ¹, obtained by adjoining an identity element to the semigroup generated by two idempotents a and b subjected to the relation 0=abab ⋯ (length ℓ). We also prove a syntactic sufficient condition which is equivalent to the sufficient condition of Lee under which a semigroup is non-finitely based. This gives a new proof to the results of Zhang-Luo and Lee that the semigroup L_ℓ is non-finitely based each ℓ ≥ 3.

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