Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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INDUCTIVE LIMIT IN THE CATEGORY OF C* -TERNARY RINGS

  • Received : 2021.12.30
  • Accepted : 2022.05.25
  • Published : 2023.01.31
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Abstract

We show the existence of inductive limit in the category of C*-ternary rings. It is proved that the inductive limit of C*-ternary rings commutes with the functor 𝓐 in the sense that if (Mn, ϕn) is an inductive system of C*-ternary rings, then $\lim_{\rightarrow}$ 𝓐(Mn) = 𝓐$(\lim_{\rightarrow}\;M_{n})$. Some local properties (such as nuclearity, exactness and simplicity) of inductive limit of C*-ternary rings have been investigated. Finally we obtain $\lim_{\rightarrow}\;M_{n}^{**}$ = $(\lim_{\rightarrow}\;M_{n})^{**}$.

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Acknowledgement

The research of the first author is supported by the National Board of Higher Mathematics(NBHM), Government of India. The second author acknowledges support from National Academy of Sciences, India. The authors are indebted to the referee for a careful reading of the manuscript and for valuable comments and suggestions.

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