Green’s relations, regularity and abundancy for semigroups of quasi-onto transformations

Mendes-Gonçalves, Suzana

doi:10.1007/s00233-014-9637-5

Cited by 3 publications

(3 citation statements)

References 3 publications

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“…We note that Mendes-Gonçalves [7] described Green's relations L, R, and D in the semigroups AE (X, q) = {α ∈ T (X) :…”

Section: Green's Relationsmentioning

confidence: 99%

The Semigroup of Surjective Transformations on an Infinite Set

Konieczny

2019

Algebra Colloq.

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For an infinite set X, denote by Ω(X) the semigroup of all surjective mappings from X to X. We determine Green’s relations in Ω(X), show that the kernel (unique minimum ideal) of Ω(X) exists and determine its elements and cardinality. For a countably infinite set X, we describe the elements of Ω(X) for which the 𝒟-class and 𝒥-class coincide. We compare the results for Ω(X) with the corresponding results for other transformation semigroups on X.

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“…We note that Mendes-Gonçalves [7] described Green's relations L, R, and D in the semigroups AE (X, q) = {α ∈ T (X) :…”

Section: Green's Relationsmentioning

confidence: 99%

The Semigroup of Surjective Transformations on an Infinite Set

Konieczny

2019

Algebra Colloq.

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“…Many nonregular classes of transformation semigroups were shown to be either abundant or adequate, for example see [4ś7, 16,23,30,32]. Recently, AlKharousi et al have shown that the semigroup OCI n , of all order preserving one to one contraction maps of a őnite chain is adequate [14].…”

Section: Starred Green's Relationsmentioning

confidence: 99%

On certain semigroups of contraction mappings of a finite chain

Umar

Zubairu

2021

ADM

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Let[n] ={1,2, . . . , n} be a finite chain and let Pn (resp.,Tn) be the semigroup of partial transformations on[n] (resp., full transformations on[n]). Let CPn={α∈ Pn: (for allx, y ∈ Dom α)|xα−yα|⩽|x−y|}(resp., CTn={α∈ Tn: (for allx, y∈[n])|xα−yα|⩽|x−y|}) be the subsemigroup of partial contractionmappings on[n](resp., subsemigroup of full contraction mappingson[n]). We characterize all the starred Green’s relations on C Pn and it subsemigroup of order preserving and/or order reversingand subsemigroup of order preserving partial contractions on[n], respectively. We show that the semigroups CPn and CTn, and some of their subsemigroups are left abundant semigroups for all n but not right abundant forn⩾4. We further show that the set ofregular elements of the semigroup CTn and its subsemigroup of order preserving or order reversing full contractions on[n], each formsa regular subsemigroup and an orthodox semigroup, respectively.

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“…Many nonregular classes of transformation semigroups were shown to be either abundant or adequate, for example see [18,19,20,21,15,16,22,14]. Recently, AlKharousi et al have shown that the semigroup OCI n , of all order preserving one to one contraction maps of a finite chain is adequate [3].…”

Section: Starred Green's Relationsmentioning

confidence: 99%

On certain semigroups of partial contractions of a finite chain

Umar,

Zubairu

2018

Preprint

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Let [n] = {1, 2, . . . , n} be a finite chain and let Pn be the semigroup of partial transformations on [n]. Let CPn = {α ∈ Pn : (f or all x, y ∈ Dom α) |xα − yα| ≤ |x − y|} be the subsemigroup of partial contraction mappings on [n]. We have shown that the semigroup CPn and some of its subsemigroups are nonregular left abundant semigroups for all n but not right abundant for n ≥ 4.

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Green’s relations, regularity and abundancy for semigroups of quasi-onto transformations

Cited by 3 publications

References 3 publications

The Semigroup of Surjective Transformations on an Infinite Set

The Semigroup of Surjective Transformations on an Infinite Set

On certain semigroups of contraction mappings of a finite chain

On certain semigroups of partial contractions of a finite chain

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