Permutative Semigroups Whose Congruences Form a Chain
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Semigroups whose congruences form a chain are often termed Δ-semigroups. The commutative Δ-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative Δ-semigroups. It turns out that there are only six noncommutative examples, each of which has at most three elements.
KeywordsNatural Generalization Permutational Identity Permutative Semigroup
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