Finite Semigroups Satisfying an Identity x₁ … x_n ≈ ρ(x₁, …, x_n)

2025/09/23 by Alexander Thumm, Thumm, Alexander
Computer Science · Mathematics · #semigroups and automata theory #Commutative Algebra and Its Applications #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2509.19216

Abstract

We determine the maximal pseudovarieties of finite semigroups that satisfy an identity of the form x₁ … x_n ≈ ρ(x₁, …, x_n). Applying this classification, we further show that a pseudovariety of permutative semigroups satisfies a common permutation identity if and only if it satisfies an identity of the above form or, equivalently, if it does not contain T = [x² ≈ xyx ≈ 0].

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