| 控制维数大于等于2的右Artin代数 |
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| 引用本文： | 李爱华,郭晋云,黎奇升.控制维数大于等于2的右Artin代数[J].南京大学学报(自然科学版),2014,31(2):190-203. |
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| 作者姓名： | 李爱华 郭晋云 黎奇升 |
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| 作者单位： | 1. 吉首大学数学与统计学院,吉首,416000
2. 湖南师范大学数学与计算机科学学院,长沙,410007 |
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| 摘 要： | 作者在文11中对单项式代数进行了推广,并定义了一类新的代数-无交换关系代数.本文证明了控制维数大于等于2的右Artin代数∧是Nakayama,代数当且仅当∧是无交换关系代数,从而在此类代数上证明了Nakayama猜想和AuslanderReiten猜想.
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| 关 键 词： | 无交换关系代数 控制维数 Nakayama猜想 Auslander-Reiten猜想 |
RIGHT ARTIN ALGEBRAS WITH DOMINANT DIMENSIONS LARGER THAN OR EQUAL TO 2 |
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| Li Aihua,Guo Jinyun,Li Qisheng.RIGHT ARTIN ALGEBRAS WITH DOMINANT DIMENSIONS LARGER THAN OR EQUAL TO 2[J].Journal of Nanjing University: Nat Sci Ed,2014,31(2):190-203. |
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| Authors: | Li Aihua Guo Jinyun Li Qisheng |
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| Institution: | Li Aihua;Guo Jinyun;Li Qisheng;College of Mathematics and Statistics,Jishou University;College of Mathematics and Computer Sciences,Hunan Normal University; |
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| Abstract: | This paper proves that the right artin algebra with dominant dimensions larger than or equal to 2 is the Nakayama algebra if and only if it is the algebra with no commutative relations,which is a generalization of monomial algebras and introduced in1]by the author.Thus the Nakayama conjecture and Auslander-Reiten conjecture are proved on this kind of algebras. |
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| Keywords: | algebras with no commutative relations the dominant dimension Nakayama conjectures Auslander-Reiten conjectures |
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