A Note on Free Idempotent Generated Semigroups over the Full Monoid of Partial Transformations

DOI10.1080/00927872.2011.607875zbMath1267.20091arXiv1101.3057OpenAlexW3100572838MaRDI QIDQ4916419

Igor Dolinka

Publication date: 22 April 2013

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.3057

zbMATH Keywords

idempotentsmaximal subgroupssemigroups of partial transformationsfree idempotent generated semigroupsidempotent transformations

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Free semigroups, generators and relations, word problems (20M05)

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Free idempotent generated semigroups: subsemigroups, retracts and maximal subgroups ⋮ A groupoid approach to regular \(\ast \)-semigroups ⋮ A group-theoretical interpretation of the word problem for free idempotent generated semigroups ⋮ Free idempotent generated semigroups: the word problem and structure via gain graphs ⋮ Presentations for singular wreath products ⋮ Free idempotent generated semigroups and endomorphism monoids of free \(G\)-acts. ⋮ Elaborating the word problem for free idempotent-generated semigroups over the full transformation monoid ⋮ The Mathematical Work of K. S. S. Nambooripad

Cites Work

• Classical finite transformation semigroups. An introduction.
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• The biorder on the partial groupoid of idempotents of a semigroup
• Idempotent-generated completely O-simple semigroups
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• Presentations for subgroups of monoids
• Subgroups of free idempotent generated semigroups need not be free.
• Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid
• SUBGROUPS OF THE FREE SEMIGROUP ON A BIORDERED SET IN WHICH PRINCIPAL IDEALS ARE SINGLETONS
• The Subsemigroup Generated By the Idempotents of a Full Transformation Semigroup