• Title/Summary/Keyword: Finite von Neumann algebra

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PROPERTY T FOR FINITE VON NEUMANN ALGEBRAS

  • Boo, Deok-Hoon;Park, Chun-Gil
    • Journal of the Chungcheong Mathematical Society
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    • v.10 no.1
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    • pp.117-126
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    • 1997
  • We find more simple forms of property T for von Neumann algebras which are finite direct sum of $II_1$ factors.

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ON ALMOST QUASI-COHERENT RINGS AND ALMOST VON NEUMANN RINGS

  • El Alaoui, Haitham;El Maalmi, Mourad;Mouanis, Hakima
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.5
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    • pp.1177-1190
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    • 2022
  • Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α1, …, αp and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and AnnRm) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αn, bn) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.

FREE PROBABILITY THEORY AND ITS APPLICATION

  • Heo, Jaeseong
    • Journal of the Chungcheong Mathematical Society
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    • v.15 no.2
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    • pp.13-23
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    • 2003
  • We prove a simplicity of the $C^*$-algebra generated by some $C^*$-subalgebra and a Haar unitary in a free product of finite von Neumann algebras. Some examples and questions are given.

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