The Experts below are selected from a list of 1707 Experts worldwide ranked by ideXlab platform
Jochen Glück - One of the best experts on this subject based on the ideXlab platform.
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Square roots and continuity in strictly linearly ordered Semigroups on real intervals
Semigroup Forum, 2014Co-Authors: Jochen GlückAbstract:In this article we show that the Semigroup Operation of a strictly linearly ordered Semigroup on a real interval is automatically continuous if each element of the Semigroup admits a square root. Hence, by a result of Aczél, such a Semigroup is isomorphic to an additive subSemigroup of the real numbers.
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Square Roots and Continuity in Strictly Linearly Ordered Semigroups on Real Intervals
Semigroup Forum, 2014Co-Authors: Jochen GlückAbstract:In this article we show that the Semigroup Operation of a strictly linearly ordered Semigroup on a real interval is automatically continuous if each element of the Semigroup admits a square root. Hence, by a result of Acz\'el, such a Semigroup is isomorphic to an additive subSemigroup of the real numbers.
Ondřej Klíma - One of the best experts on this subject based on the ideXlab platform.
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Pseudovarieties of Ordered Completely Regular Semigroups
Results in Mathematics, 2019Co-Authors: Jorge Almeida, Ondřej KlímaAbstract:This paper is a contribution to the theory of finite Semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role is played by the consideration of an order compatible with the Semigroup Operation. In the case of unions of groups, so-called completely regular Semigroups, the problem of which new pseudovarieties appear in the ordered context is solved. As applications, it is shown that the lattice of pseudovarieties of ordered completely regular Semigroups is modular and that taking the intersection with the pseudovariety of bands defines a complete endomorphism of the lattice of all pseudovarieties of ordered Semigroups.
Reinhard Suck - One of the best experts on this subject based on the ideXlab platform.
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The structure of rating scales
Journal of Mathematical Psychology, 2018Co-Authors: Reinhard SuckAbstract:Abstract The structure of the set of all possible rating scales is investigated. It is shown that by a natural addition of rating scales the set is a commutative Semigroup with neutral element. From this Operation a partial order can be defined which turns out to a lattice order. This lattice is shown to be distributive. In the next step two possibilities –closely related to the preceding development –are analyzed to endow this structure with a metric. The Semigroup Operation is shown to be continuous in the respective topologies. With the help of one of these metrics the question of the scale type of rating scales is discussed by giving the concept of admissible transformations an extended meaning.
Hirokazu Oka - One of the best experts on this subject based on the ideXlab platform.
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Semigroup Operations distributed by natural noncancellative Semigroup Operations on the positive real numbers
Semigroup Forum, 2020Co-Authors: Hirokazu Oka, Takeshi Miura, Sin-ei TakahasiAbstract:Let $${\mathbf {R}}_+$$ R + be the space of positive real numbers with the ordinary topology. Let $$\star $$ ⋆ be the natural noncancellative continuous Semigroup Operation $$\times $$ × or $$\diamond $$ ⋄ on $${\mathbf {R}}_+$$ R + as defined in first section. We characterize the set $${\mathcal {D}}_\star ({\mathbf {R}}_+)$$ D ⋆ ( R + ) of all cancellative continuous Semigroup Operations on $${\mathbf {R}}_+$$ R + which are distributed by $$\star $$ ⋆ in terms of homeomorphism. As a consequence, we show that an arbitrary Semigroup Operation in $${\mathcal {D}}_\star ({\mathbf {R}}_+)$$ D ⋆ ( R + ) is homeomorphically isomorphic to the ordinary multiplication on $${\mathbf {R}}_+$$ R + .
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Characterization of distributive Semigroup Operations on the positive real numbers
Semigroup Forum, 2020Co-Authors: Sin-ei Takahasi, Takeshi Miura, Hirokazu OkaAbstract:Given any cancellative continuous Semigroup Operation $$\star $$ ⋆ on the positive real numbers $$\mathbf {R}_+$$ R + with the ordinary topology, we completely characterize the set $$\mathcal {D}_\star (\mathbf {R}_+)$$ D ⋆ ( R + ) of all cancellative continuous Semigroup Operations on $$\mathbf {R}_+$$ R + which are distributed by $$\star $$ ⋆ in terms of homeomorphism. As a consequence, we show that an arbitrary Semigroup Operation in $$\mathcal {D}_\star (\mathbf {R}_+)$$ D ⋆ ( R + ) is homeomorphically isomorphic to the ordinary addition $$+$$ + on $$\mathbf {R}_+$$ R + .
Jorge Almeida - One of the best experts on this subject based on the ideXlab platform.
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Pseudovarieties of Ordered Completely Regular Semigroups
Results in Mathematics, 2019Co-Authors: Jorge Almeida, Ondřej KlímaAbstract:This paper is a contribution to the theory of finite Semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role is played by the consideration of an order compatible with the Semigroup Operation. In the case of unions of groups, so-called completely regular Semigroups, the problem of which new pseudovarieties appear in the ordered context is solved. As applications, it is shown that the lattice of pseudovarieties of ordered completely regular Semigroups is modular and that taking the intersection with the pseudovariety of bands defines a complete endomorphism of the lattice of all pseudovarieties of ordered Semigroups.
