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Generators and factorisations of transformation semigroups

  • Peter M. Higgins (a1), John M. Howie (a2) and Nikola Ruškuc (a2)

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If E is the set of idempotents and G the group of units within a full transformation semigroup ℐx, then EG = GE = ℐx if X is finite. The question of identifying the subsemigroup EG = GE = 〈G∪E〉 in the case where X is infinite leads to an investigation of interrelations among various naturally occurring subsemigroups of X. In the final section it is shown that precisely two additional elements µ, v are needed in order that G∪E∪{µ, v} should generate x.

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References

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Generators and factorisations of transformation semigroups

  • Peter M. Higgins (a1), John M. Howie (a2) and Nikola Ruškuc (a2)

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