On relative ranks of full transformation semigroups

DOI10.1080/00927879808826160zbMath0902.20027OpenAlexW2094512319MaRDI QIDQ4395710

Peter M. Higgins, John M. Howie, Nikola Ruškuc

Publication date: 6 December 1998

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

Full work available at URL: https://doi.org/10.1080/00927879808826160

zbMATH Keywords

idempotentsgenerating setsgroups of unitsfull transformation semigroupsregular cardinalssingular cardinalssurjectionsinjectionscontraction index

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Free semigroups, generators and relations, word problems (20M05) Large cardinals (03E55) Other classical set theory (including functions, relations, and set algebra) (03E20) Ordinal and cardinal numbers (03E10)

Related Items (34)

The semigroup generated by the idempotents of a partition monoid. ⋮ Ranks of ideals in inverse semigroups of difunctional binary relations ⋮ Semigroups of rectangular matrices under a sandwich operation ⋮ Relative ranks in the monoid of endomorphisms of an independence algebra. ⋮ On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range ⋮ Polymorphism clones of homogeneous structures: generating sets, Sierpiński rank, cofinality and the Bergman property ⋮ The rank of the endomorphism monoid of a uniform partition. ⋮ Motzkin monoids and partial Brauer monoids ⋮ Generating Borel measurable mappings with continuous mappings ⋮ Idempotents and one-sided units: lattice invariants and a semigroup of functors on the category of monoids ⋮ Relative ranks of Lipschitz mappings on countable discrete metric spaces ⋮ The relative rank of the endomorphism monoid of a finite \(G\)-set ⋮ Centralizers in the full transformation semigroup. ⋮ The rank of the semigroup of transformations stabilising a partition of a finite set ⋮ A note on generators of the endomorphism semigroup of an infinite countable chain ⋮ SPECTRUM CONVOLUTION OF FULL TRANSFORMATION SEMIGROUP ⋮ Infinite dual symmetric inverse monoids ⋮ Generation of infinite factorizable inverse monoids. ⋮ John Macintosh Howie: work and legacy ⋮ Permutations of a semigroup that map to inverses. ⋮ A finite interval in the subsemigroup lattice of the full transformation monoid. ⋮ Unnamed Item ⋮ Sandwich semigroups in locally small categories. I: Foundations ⋮ On relative ranks of the semigroup of orientation-preserving transformations on infinite chains ⋮ Unnamed Item ⋮ Structure of principal one-sided ideals ⋮ Generating the infinite symmetric group using a closed subgroup and the least number of other elements ⋮ On relative ranks of finite transformation semigroups with restricted range ⋮ Idempotents and one-sided units in infinite partial Brauer monoids ⋮ On orientation-preserving transformations of a chain ⋮ Maximal subsemigroups of the semigroup of all mappings on an infinite set ⋮ Generating continuous mappings with Lipschitz mappings ⋮ Sandwich semigroups in diagram categories ⋮ Infinite partition monoids

Cites Work

• Unnamed Item
• On the ranks of certain semigroups of order-preserving transformations
• Green's equivalences in finite semigroups of binary relations
• Matrix semigroups -- generators and relations
• Idempotent rank in finite full transformation semigroups
• On the ranks of certain finite semigroups of transformations
• On the nilpotent ranks of certain semigroups of transformations
• On the rank of completely 0-simple semigroups
• The Subsemigroup Generated By the Idempotents of a Full Transformation Semigroup

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