대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권1호
  • /
  • Pages.123-135
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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REPRESENTATIONS OF C*-TERNARY RINGS

  • Arpit Kansal (Department of Mathematics University Of Delhi) ;
  • Ajay Kumar (Department of Mathematics University Of Delhi) ;
  • Vandana Rajpal (Department of Mathematics Shivaji College)
  • 투고 : 2021.12.30
  • 심사 : 2022.07.28
  • 발행 : 2023.01.31
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초록

It is proved that there is a one to one correspondence between representations of C*-ternary ring M and C*-algebra 𝒜(M). We discuss primitive and modular ideals of a C*-ternary ring and prove that a closed ideal I is primitive or modular if and only if so is the ideal 𝒜(I) of 𝒜(M). We also show that a closed ideal in M is primitive if and only if it is the kernel of some irreducible representation of M. Lastly, we obtain approximate identity characterization of strongly quasi-central C*-ternary ring and the ideal structure of the TRO V ⊗tmin B for a C*-algebra B.

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과제정보

Research of the first author is supported by the National Board of Higher Mathematics(NBHM), Government of India. Second author acknowledges support from National Academy of Sciences, India. Authors are grateful to the referee for some useful comments.

참고문헌

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