Interassociates of the bicyclic semigroup

Givens, Berit Nilsen; Rosin, Amber; Linton, Karen

doi:10.1007/s00233-016-9794-9

Cited by 10 publications

(8 citation statements)

References 2 publications

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“…It was shown that for distinct pairs (m, n) and (s, t), the interassociates (C (p, q), * m,n ) and (C (p, q), * s,t ) are not isomorphic. Also in [24] the authors generalized a result regarding homomorphisms on C (p, q) to homomorphisms on its interassociates. Later for fixed non-negative integers m and n the interassociate (C (p, q), * m,n ) of the bicyclic monoid C (p, q) will be denoted by C m,n .…”

Section: Introductionmentioning

confidence: 95%

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On variants of the extended bicyclic semigroup

Гутік¹,

Maksymyk²

2018

Preprint

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In the paper we describe the group Aut (C Z ) of automorphisms of the extended bicyclic semigroup C Z and study the variants C m,n Z of the extended bicycle semigroup C Z , where m, n ∈ Z. In particular, we prove that Aut (C Z ) is isomorphic to the additive group of integers, the extended bicyclic semigroup C Z and every its variant are not finitely generated, and describe the subset of idempotents E(C m,n Z ) and Green's relations on the semigroup C m,n Z . Also we show that E(C m,n Z) is an ω-chain and any two variants of the extended bicyclic semigroup C Z are isomorphic. At the end we discuss shiftcontinuous Hausdorff topologies on the variant C 0,0 Z . In particular, we prove that if τ is a Hausdorff shift-continuous topology on C 0,0 Z then each of inequalities a > 0 or b > 0 implies that (a, b) is an isolated point of C 0,0 Z , τ and construct an example of a Hausdorff semigroup topology τ * on the semigroup C 0,0 Z such that all its points with ab 0 and a + b 0 are not isolated in C 0,0 Z , τ * .

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Section: Introductionmentioning

confidence: 95%

“…In the paper [24] the bicyclic semigroup C (p, q) and its interassociates are investigated. In particular, if p and q are generators of the bicyclic semigroup C (p, q) and m and n are fixed nonnegative integers, the operation a * m,n b = a • q m p n • b is known to be an interassociate.…”

Section: Introductionmentioning

confidence: 99%

On variants of the extended bicyclic semigroup

Гутік¹,

Maksymyk²

2018

Preprint

View full text Add to dashboard Cite

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“…It was shown that for distinct pairs (m, n) and (s, t), the interassociates (C (p, q), * m,n ) and (C (p, q), * s,t ) are not isomorphic. Also in [16] the authors generalized a result regarding homomorphisms on C (p, q) to homomorphisms on its interassociates.…”

mentioning

confidence: 95%

“…In the paper [16] the bicyclic semigroup C (p, q) and its interassociates are investigated. In particular, if p and q are generators of the bicyclic semigroup C (p, q) and m and n are fixed nonnegative integers, the operation a * m,n b = aq m p n b is known to be an interassociate.…”

mentioning

confidence: 99%

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On semitopological interassociates of the bicyclic monoid

Gutik,

Maksymyk

2016

Preprint

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Semitopological interassociates C m,n of the bicyclic semigroup C (p, q) are studied. In particular, we show that for arbitrary non-negative integers m, n and every Hausdorff topology τ on C m,n such that (C m,n , τ ) is a semitopological semigroup, is discrete. Also, we prove that if an interassociate of the bicyclic monoid C m,n is a dense subsemigroup of a Hausdorff semitopological semigroup (S, •) and I = S \ C m,n = ∅ then I is a two-sided ideal of the semigroup S and show that for arbitrary non-negative integers m, n, any Hausdorff locally compact semitopological semigroup C 0 m,n = C m,n ⊔ {0} is either discrete or compact.

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Free Products of n-Tuple Semigroups

Zhuchok

Koppitz

2019

Ukr Math J

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Interassociates of the bicyclic semigroup

Cited by 10 publications

References 2 publications

On variants of the extended bicyclic semigroup

On variants of the extended bicyclic semigroup

On semitopological interassociates of the bicyclic monoid

Free Products of n-Tuple Semigroups

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