摘要
文章从简单的余模范畴中的正合列入手,一方面分析了遗传artin余代数,利用长度公式定义了同调二次型及正定二次型,并讨论同调二次型满足正定性所需条件及相应结果;另一方面研究遗传anin余代数的有限表示型的一些必要条件,并逐渐与同调二次型的正定性相联系;最后构造遗传artin余代数上的同调二次型正定性与有限表示型之间的充分必要关系．
Starting with simple exact sequence in category of comodules, this article studies three problems on artin coalgebras. Firstly, using length formula, it analyses the hereditary artin coalgebras, defines the homological quadratic and positive defined quadratic, and discusses the required conditions and correspond results which homological quadratic satisfies positive definiteness; secondly, it researches the necessary conditions of finite representation type of hereditary artin coalgebras and relates to positive definiteness of homological quadratic; at last, it constructs the necessary and sufficient condition between the positive definiteness of homological quadratic and finite representation type.
出处
《襄樊学院学报》
2006年第2期16-18,共3页
Journal of Xiangfan University
关键词
同调二次型
artin余代数
可裂扩张
The homological quadratic form
Artin-coalgebras
Split extension
