Sep, 2015
Global dimension of Harada rings and serial rings
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
- Volume
- 14
- Number
- 7
- Language
- English
- Publishing type
- Research paper (scientific journal)
- DOI
- 10.1142/S0219498815501157
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
Baba [On Harada rings and quasi-Harada rings with left global dimension at most 2. Comm. Algebra 28(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.
- Link information
- ID information
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- DOI : 10.1142/S0219498815501157
- ISSN : 0219-4988
- eISSN : 1793-6829
- Web of Science ID : WOS:000353552200018