Global dimension of Harada rings and serial rings
Global dimension of Harada rings and serial rings
复制标题
原田戒指和系列戒指的全球尺寸
DOI：
10.1142/s0219498815501157
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发表时间：
2015
影响因子：
0.8
通讯作者：
Kazutoshi Koike
中科院分区：
文献类型：
--
作者：
M. Hoshino;N. Kameyama and H. Koga;酒井文雄;尾形庄悦;川崎 謙一郎;Kazutoshi Koike
Baba[关于左全局维数不超过2.Comm的原田环和拟原田环。]代数28(6)(2000)2671-2684]证明了每一个全局维数不超过2的左Harada环都是序列环。在此基础上，进一步证明了每一个全局维数不超过3的左原田环都是一个序列环。证明了有限整体维数的左原田环a是（*）型或具有齐次右环，则a是串行的。最后给出了有限整体维数的非序列左原田环的一个例子。
Baba [On Harada rings and quasi-Harada rings with left global dimension at most 2.Comm. Algebra28(6) (2000) 2671–2684] proved that every left Harada rings with global dimension at most 2 is a serial ring. In this paper, improving the result, we show that every left Harada ring with global dimension at most 3 is a serial ring. We also prove that if a left Harada ring A of finite global dimension is of type (*) or has homogeneous right socle, then A is serial. Finally, we give an example of a non-serial left Harada ring of finite global dimension.