• Title/Summary/Keyword: weakly Abelian

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WEAK AMENABILITY OF CONVOLUTION BANACH ALGEBRAS ON COMPACT HYPERGROUPS

  • Samea, Hojjatollah
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.307-317
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    • 2010
  • In this paper we find necessary and sufficient conditions for weak amenability of the convolution Banach algebras A(K) and $L^2(K)$ for a compact hypergroup K, together with their applications to convolution Banach algebras $L^p(K)$ ($2\;{\leq}\;p\;<\;{\infty}$). It will further be shown that the convolution Banach algebra A(G) for a compact group G is weakly amenable if and only if G has a closed abelian subgroup of finite index.

Ergodic properties of compact actions on $C^{+}$-algebras

  • Jang, Sun-Young
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.289-295
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    • 1994
  • Let (A,G,.alpha.) be a $C^{*}$-dynamical system. In [3] the classical notions of ergodic properties of topological dynamical systems such as topological transitivity, minimality, and uniquely ergodicity are extended and analyzed in the context of non-abelian $C^{*}$-dynamical systems. We showed in [2] that if G is a compact group, then minimality, topological transitivity, uniquely ergodicity, and weakly ergodicity of the $C^{*}$-dynamical system (A,G,.alpha.) are equivalent.alent.

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ORDERED GROUPS IN WHICH ALL CONVEX JUMPS ARE CENTRAL

  • Bludov, V.V.;Glass, A.M.W.;Rhemtulla, Akbar H.
    • Journal of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.225-239
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    • 2003
  • (G, <) is an ordered group if'<'is a total order relation on G in which f < g implies that xfy < xgy for all f, g, x, y $\in$ G. We say that (G, <) is centrally ordered if (G, <) is ordered and [G,D] $\subseteq$ C for every convex jump C $\prec$ D in G. Equivalently, if $f^{-1}g f{\leq} g^2$ for all f, g $\in$ G with g > 1. Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.

ON RIGHT QUASI-DUO RINGS WHICH ARE II-REGULAR

  • Kim, Nam-Kyun;Lee, Yang
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.217-227
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    • 2000
  • This paper is motivated by the results in [2], [10], [13] and [19]. We study some properties of generalizations of commutative rings and relations between them. We also show that for a right quasi-duo right weakly ${\pi}-regular$ ring R, R is an (S,2)-ring if and only if every idempotent in R is a sum of two units in R, which gives a generalization of [2, Theorem 4] on right quasi-duo rings. Moreover we find a condition which is equivalent to the strongly ${\pi}-regularity$ of an abelian right quasi-duo ring.

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A KIND OF NORMALITY RELATED TO REGULAR ELEMENTS

  • Huang, Juan;Piao, Zhelin
    • Honam Mathematical Journal
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    • v.42 no.1
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    • pp.93-103
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    • 2020
  • This article concerns a property of Abelain π-regular rings. A ring R shall be called right quasi-DR if for every a ∈ R there exists n ≥ 1 such that C(R)an ⊆ aR, where C(R) means the monoid of regular elements in R. The relations between the right quasi-DR property and near ring theoretic properties are investigated. We next show that the class of right quasi-DR rings is quite large.