Nuclear C~*-代数中的三角子代数的根

RADICALS OF TRIANGULAR SUBALGEBRAS OF NUCLEAR C * ALGEBRAS WITH DIAGONALS

设Ｂ是含Ｋｕｍｊｉａｎ意义的对角Ｄ的ＮｕｃｌｅａｒＣ＊－代数．Ａ是Ｂ中的三角子代数，本文讨论Ａ的各种根之间的关系．特别的，证明了Ａ的Ｊａｃｏｂｓｏｎ根等于Ａ的拓扑素根，拓扑原始根等于Ａ的素根的闭包．

Let A be a triangular subalgebra of nuclear C * algebra B with diagonal D in the sense of Kumjian. This paper discussed the relationship among the radicals of A. Particularly, it is proved that the Jacobson radical of A coincides with the topological prime redical of A, and the topological primal radical of A conincides with the closure of the prime radical of A.