C-正交有限代数的广义Nakayama猜想
Generalized Nakayama Conjecture for C-Orthogonal-Finite Algebras
摘要: 给出了C-正交有限代数的定义并证明了任意的C-正交有限代数满足广义Nakayama猜想。由此可得到Gorenstein CM-有限代数满足广义Nakayama猜测。
Abstract: In this paper, the C-orthogonal-finite algebras are defined. Moreover, the generalized Nakayama conjecture is proved to be true for C-orthogonal-finite algebras. As a result, Gorenstein CM-finite algebras satisfy the generalized Nakayama conjecture.
文章引用：张孝金. C-正交有限代数的广义Nakayama猜想[J]. 理论数学, 2013, 3(1): 1-3. http://dx.doi.org/10.12677/PM.2013.31001

参考文献

[1] M. Auslander, I. Reiten. On a generalized version of the Nakayama conjecture. Proceedings of the American Mathematical Society, 1975, 52(1): 69-74.
[2] M. Auslander, I. Reiten. Applications of contravariantly finite subcategories. Advances in Mathematics, 1991, 86(1): 111-152.
[3] K. Yamagata. Frobineus algebras. Handbook of Algebra, 1980, 1: 841-887.
[4] K. R. Fuller, B. Zimmermann-Huisgen. On the generalized Nakayama conjecture and the Cartan determinant problem. Transactions of the American Mathematical Society, 1986, 294(2): 679-691.
[5] A. Maróti. A proof of a generalized Nakayama conjecture. Bulletin London Mathematical Society, 2006, 38(5): 777-785.
[6] G. Wilson. The Cartan map on categories of graded modules. Journal of Algebra, 1983, 85: 390-398.
[7] R. Luo, Z. Y. Huang. When are torsionless modules projective? Journal of Algebra, 2008, 320(5): 2156-2164.
[8] E. E. Enochs, O. M. G. Jenda. Gorenstein injective and projective modules. Mathematische Zeitschrift, 1995, 220(1): 611-633.
[9] X. W. Chen. An Auslander-type result for Gorenstein-projective modules. Advances in Mathematics, 2008, 208(6): 2043-2050.
[10] Z.-W. Li, P. Zhang. Gorenstein algebras of finite Cohen-Macaulay type. Advances in Mathematics, 2010, 223(2): 728-734.
[11] Z.-W. Li, P. Zhang. A construction of Gorenstein-projective modules. Journal of Algebra, 2010, 323(6): 1802-1812.
[12] A. Beligiannis. On algebras of finite Cohen-Macaulay type. Advances in Mathematics, 2011, 226(2): 1973-2019.

为你推荐