控制维数大于等于2的右Artin代数

RIGHT ARTIN ALGEBRAS WITH DOMINANT DIMENSIONS LARGER THAN OR EQUAL TO 2

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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. 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 in[1]by the author.Thus the Nakayama conjecture and Auslander-Reiten conjecture are proved on this kind of algebras.

作者李爱华郭晋云黎奇升

机构地区吉首大学数学与统计学院湖南师范大学数学与计算机科学学院

出处《南京大学学报（数学半年刊）》 CAS 2014年第2期190-203,共14页 Journal of Nanjing University(Mathematical Biquarterly)

基金国家自然科学基金(11271119 11201177)资助

关键词无交换关系代数控制维数 Nakayama猜想 Auslander-Reiten猜想 algebras with no commutative relations the dominant dimension Nakayama conjectures Auslander-Reiten conjectures

分类号 O153 [理学—基础数学]

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1李爱华,黎奇升.单项代数的一种推广[J].南京大学学报（数学半年刊）,2011,28(2):195-205. 被引量：1
2Igusa K and Zacharia D. Syzygy Pairs in a Monomial Algebra. Proc. Amer. Math. Soc., 1990, 108: 601-604.
3Grenn E L and Zimmermann-Huisgen B. Finitistic Dimension of Artinian Rings with Vanishing Radical Cube. Math. Z., 1991, 206: 505-526.
4Anick D. On Monomial Algebras of Finite Global Dimension. Trans. A.M.S., 1985, 291(1): 291-310.
5Anick D and Grenn E L. On the Homology of Quotients of Path Algebras. Comm. in Algebra, 1987, 15(1-2): 309-341.
6Auslander M, Reiten I and Smal S. Representation Theory of Artin Algebras. London: Cambridge University Press., 1995.
7Nakayama T. On Algebras with Complete Homology. Abh. Math. Sem. Univ. Hamburg, 1958, 22 300-307.
8Guo J Y. Auslander Reiten Conjecture and Functor Jk2 . Arch. Math., 1998, 70: 351-356.

二级参考文献9

1Igusa K and Zacharia D. Syzygy Pairs in a Monomial Algebra. Proc. Amer. Math. Soc., 1990, 108: 601-604.
2Anick D. On Monomial Algebras of Finite Alobal Dimension. Trans. A. M. S., 1985, 291(1): 291-310.
3Anick D and Green E L. On the Homology of Quotients of Path Algebra. Comm. in Algebra, 1987, 15(1): 309-341.
4Green E L, Happel D and Zacharia D. Projective Resolutions over Artin Algebras with Zero Rela- tions. Illinois J. Math., 1985, 92: 180-190.
5Wilson G V. The Cartan Map on Categories of Graded Modules. J. Algebra, 1983, 85: 390-398.
6Zimmermann-Huisgen B. Predicting Syzygies over Monomial Relations Algebras. Manuscipta Math., 1991, 70: 157-182.
7Burgess W D, Fuller K R, Green E L and Zacharia D. Left Monomial Rings- a Generalization of Monomial Algebras. Osaka J. Math., 1993, 30: 543-558.
8Auslander M, Reiten I and Smalo S O. Representation Theory of Artin Algebras. Cambridge Studies in Advanced Mathematics 36, Cambridge Univ. Press, 1995.
9Green E L, Kirkman E and Kuzmanovich J. Finitistic Dimensions of Finite Dimensional Monomial Algebras. J. Algebra, 1991, 136: 37-50.

1吴俊.相对控制维数[J].芜湖职业技术学院学报,2006,8(3):4-6.
2杜先能,葛茂荣.相关于函子Ext^i（—，—）的两个问题[J].南京大学学报（数学半年刊）,2004,21(1):144-148.
3徐强,双丰.量子系统的有效维数鉴别和约化理论[J].量子电子学报,2012,29(3):316-322.

南京大学学报（数学半年刊）

2014年第2期

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控制维数大于等于2的右Artin代数

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