Permutative semigroup whose congruences form a chain

Abstract

Semigroups whose congruences form a chain are often termed Δ-semigroups. The commutative Δ-semigroups were determined by Schein and 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.

Keywords: Permutative D-semigroups., non-identity, homomorphic image, abelian group

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 41 – 48