Finite basis problem for Lee monoids with involution. Issue 10 (4th August 2021) - Gao, Meng; Zhang, Wen-Ting; Luo, Yan-Feng
Abstract: For each k ≥ 2, let L k 1 denote the monoid obtained by adjoining an identity element to the semigroup generated by two idempotents E and F subjected to the relation EFEF ⋯ = 0, where the left side is a product of length k . Under a certain unary operation *, the unary monoid ( L k 1, * ) is an involution monoid. By recent results, the monoid L k 1 is non-finitely based if and only if k ≥ 3 . As for the involution monoid ( L k 1, * ), it is only known to be non-finitely based for all even k ≥ 2 . The objective of this article is to show that ( L k 1, * ) is non-finitely based for all odd k ≥ 3 . Consequently, ( L k 1, * ) is non-finitely based for all k ≥ 2 .