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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2023.1
- 수록면
- 123 - 135 (13page)
- DOI
- 10.4134/CKMS.c210437
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초록· 키워드
오류제보하기
It is proved that there is a one to one correspondence between representations of $C^{\ast}$-ternary ring $M$ and $C^{\ast}$-algebra $\mathcal{A}(M)$. We discuss primitive and modular ideals of a $C^{\ast}$-ternary ring and prove that a closed ideal $I$ is primitive or modular if and only if so is the ideal $\mathcal{A}(I)$ of $\mathcal{A}(M)$. 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 $C^{\ast}$-ternary ring and the ideal structure of the TRO $ V\otimes^{\text{\rm tmin}} B$ for a $C^{\ast}$-algebra $B$.
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