Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: In this article, the authors generalize an important theorem of Fred Galvin from the Stone-Cech compactification βT of any discrete semigroup T to any compact Hausdorff right-topological semigroup with a dense topological center, and then apply it to Ellis' semigroups to prove that a point is distal if and only if it is IP*-recurrent.
Abstract: We generalize an important theorem of Fred Galvin from the Stone-Cech compactification βT of any discrete semigroup T to any compact Hausdorff right-topological semigroup with a dense topological center; and then apply it to Ellis’ semigroups to prove that a point is distal if and only if it is IP*-recurrent, for any semiflow (T;X) with arbitrary compact Hausdorff phase space X not necessarily metrizable and with arbitrary phase semigroup T not necessarily cancelable.
7 citations
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7 citations
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TL;DR: In this article, it was shown that weak compactness of partial orbits is a necessary and sufficient condition for strong continuity of the restriction of a C0-semigroup, and that if the embedded Banach space is reflexive and the norms of the restricted semigroup operators are bounded near the initial time, then the restriction is strongly continuous.
Abstract: A linear semigroup in a Banach space induces a linear semigroup on a Banach space that can be continuously embedded in the former such that its image is invariant. This restriction need not be strongly continuous, although the original semigroup is strongly continuous. We show that norm or weak compactness of partial orbits is a necessary and sufficient condition for strong continuity of the restriction of a C0-semigroup. We then show that if the embedded Banach space is reflexive and the norms of the restricted semigroup operators are bounded near the initial time, then the restricted semigroup is strongly continuous.
7 citations
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TL;DR: In this paper, the Jacobson radical of a semigroup ring R [S ] of a commutative semigroup S is determined when S is S -homogeneous, i.e.
7 citations
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TL;DR: The relation γ is the smallest equivalence relation on S so that S/γ* is a commutative semigroup and a neighbourhood system for each element of S is defined.
Abstract: Let S be a semigroup. We consider the relation γ and its transitive closure γ*. The relation γ is the smallest equivalence relation on S so that S/γ* is a commutative semigroup. Based on the relation γ, we define a neighbourhood system for each element of S, and we present a general framework of the study of approximations in semigroups. The connections between semigroups and operators are examined.
7 citations