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Quick Martyn - One of the best experts on this subject based on the ideXlab platform.
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Automorphism groups of Linearly Ordered structures and endomorphisms of the Ordered Set ( Q ,≤) of rational numbers
'Oxford University Press (OUP)', 2019Co-Authors: Mcphee, Jillian Dawn, Mitchell, James David, Quick MartynAbstract:We investigate the structure of the monoid of endomorphisms of the Ordered Set ( Q ,≤) of rational numbers. We show that for any countable Linearly Ordered Set Ω, there are uncountably many maximal subgroups of End( Q ,≤) isomorphic to the automorphism group of Ω. We characterize those subSets X of Q that arise as a retract in ( Q ,≤) in terms of topological information concerning X. Finally, we establish that a countable group arises as the automorphism group of a countable Linearly Ordered Set, and hence as a maximal subgroup of End( Q ,≤), if and only if it is free abelian of finite rank.PreprintPostprintPeer reviewe
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Automorphism groups of Linearly Ordered structures and endomorphisms of the Ordered Set $(\mathbb{Q},{\leq})$ of rational numbers
2018Co-Authors: Mcphee, Jillian D., Mitchell, James D., Quick MartynAbstract:We investigate the structure of the monoid of endomorphisms of the Ordered Set $(\mathbb{Q},{\leq})$ of rational numbers. We show that for any countable Linearly Ordered Set $\Omega$, there are uncountably many maximal subgroups of $\operatorname{End}(\mathbb{Q},{\leq})$ isomorphic to the automorphism group of $\Omega$. We characterise those subSets $X$ of $\mathbb{Q}$ that arise as a retract in $(\mathbb{Q},{\leq})$ in terms of topological information concerning $X$. Finally, we establish that a countable group arises as the automorphism group of a countable Linearly Ordered Set, and hence as a maximal subgroup of $\operatorname{End}(\mathbb{Q},{\leq})$, if and only if it is free abelian of finite rank.Comment: 24 pages. Revised based on referee's comment
Gianluca Cassese - One of the best experts on this subject based on the ideXlab platform.
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Decomposition of supermartingales indexed by a Linearly Ordered Set
Statistics & Probability Letters, 2007Co-Authors: Gianluca CasseseAbstract:We prove a version of the Doob Meyer decomposition for supermartingales with a Linearly Ordered index Set.
Singh, Ajit Iqbal - One of the best experts on this subject based on the ideXlab platform.
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Hypergroup deformations of semigroups
'Springer Science and Business Media LLC', 2019Co-Authors: Vishvesh Kumar, Ross, Kenneth A., Singh, Ajit IqbalAbstract:We view the well-known example of the dual of a countable compact hypergroup, motivated by the orbit space of p-adic integers by Dunkl and Ramirez (Trans Am Math Soc 202:339-356, 1975), as hypergroup deformation of the max semigroup structure on the Linearly Ordered Set Z+ of the non-negative integers along the diagonal. This works as motivation for us to study hypergroups or semi convolution spaces arising from max semigroups or general commutative semigroups via hypergroup deformation on idempotents
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Hypergroup Deformations of Semigroups
'Springer Science and Business Media LLC', 2018Co-Authors: Kumar Vishvesh, Ross, Kenneth A., Singh, Ajit IqbalAbstract:We view the well-known example of the dual of a countable compact hypergroup, motivated by the orbit space of p-adic integers by Dunkl and Ramirez (1975), as hypergroup deformation of the max semigroup structure on the Linearly Ordered Set $\mathbb{Z}_+$ of the non-negative integers along the diagonal. This works as motivation for us to study hypergroups or semi convolution spaces arising from "max" semigroups or general commutative semigroups via hypergroup deformation on idempotents.Comment: 28 pages, 1 Table, This version is a truncated version with fourth section deleted from version 3, which is being developed into a separate paper. The title and abstract have been changed accordingl
Jan Plavka - One of the best experts on this subject based on the ideXlab platform.
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linear independence in bottleneck algebras
Fuzzy Sets and Systems, 1996Co-Authors: Katarina Cechlarova, Jan PlavkaAbstract:Abstract Let (R, ⪕) be a Linearly Ordered Set. A bottleneck algebra is the Set R together with two operations a ⊕ b = max {a, b} and a ⊗ b = min {a, b}. In this paper we suggest various definitions of linear independence of Sets of n-tuples over R study their characteristics and interrelations.
Martyn Quick - One of the best experts on this subject based on the ideXlab platform.
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automorphism groups of Linearly Ordered structures and endomorphisms of the Ordered Set mathbb q leq of rational numbers
arXiv: Group Theory, 2016Co-Authors: Jillian Dawn Mcphee, James D Mitchell, Martyn QuickAbstract:We investigate the structure of the monoid of endomorphisms of the Ordered Set $(\mathbb{Q},{\leq})$ of rational numbers. We show that for any countable Linearly Ordered Set $\Omega$, there are uncountably many maximal subgroups of $\operatorname{End}(\mathbb{Q},{\leq})$ isomorphic to the automorphism group of $\Omega$. We characterise those subSets $X$ of $\mathbb{Q}$ that arise as a retract in $(\mathbb{Q},{\leq})$ in terms of topological information concerning $X$. Finally, we establish that a countable group arises as the automorphism group of a countable Linearly Ordered Set, and hence as a maximal subgroup of $\operatorname{End}(\mathbb{Q},{\leq})$, if and only if it is free abelian of finite rank.