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 Exchange环的K_0群的正向凸子群格(英文) Directed Convex Subgroup Lattice of K_0 of Exchange Rings 黎奇升,佟文廷 LI Qi-sheng, TONG Wen-ting 吉首大学数学与计算机科学系,南京大学数学系 吉首,湖南 416000,南京,江苏 210093 (Dept. of Math, and Computer Science, Jishou University, Jishou, Hunan, 416000, P. R. China; Dept. of Math., Nanjing University, Nanjing, Jiangsu, 210093, P. R. China 收稿日期: 2004-04-25 出版日期: 2004-04-25
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 摘要 本文证明了:(1)Exchange环R的K_0群的正向凸子群格同构于R的稳定余有限半本原理想格;(2)稳定有限、半本原的exchange环R是单的当且仅当它是K_0-单的并且满足逼近弱s~*可比性,推广了Goodearl,Ara等人的结果。 关键词 ： exchange环,  Grothendieck群,  正向凸子群,  状态 Abstract：In this paper, we show that for an exchange ring R, the directed convex subgroup lattice of K0(R) is isomorphic to the lattice of all stably co-finite and semiprimitive ideals of R; a stably finite and semiprimitive exchange ring is simple if and only if it is K0-simple and satisfies the approximate weak s*-comparability. These generalize the corresponding results of Goodearl, Ara et al.. Key words： Grothendieck group    directed convex subgroup    state
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