山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (10): 22-26.doi: 10.6040/j.issn.1671-9352.0.2018.147
吴小英,王芳贵*
WU Xiao-ying, WANG Fang-gui*
摘要： 证明了分次版本的Enochs定理: 设A是有限生成分次R-模B的分次子模, 若对任何FP-gr-内射 R-模E, 分次同态f:A→E恒能扩张到B, 则A是有限生成的。 由此得到有限生成分次R-模M是有限表现的当且仅当对任何FP-gr-内射模E, 都有EXT1R(M,E)=0。
中图分类号:
| [1] | ENOCHS E E. A note on absolutely pure modules[J]. Canad Math Bull, 1976, 19(3):361-362. |
| [2] | GAO Zenghui, WANG Fanggui. Weak injective and weak flat modules[J]. Comm Algebra, 2015, 43:3875-3868. |
| [3] | WANG Fanggui, QIAO Lei, KIM Hwankoo. Super finitely presented modules and Gorenstein projective modules[J]. Comm Algebra, 2016, 44:4056-4072. |
| [4] | WANG Fanggui, KIM Hwankoo. Foundations of commutative rings and their modules[M]. Singapore: Springer, 2016. |
| [5] | STENSTRÖM B. Coherent rings and FP-injective modules[J]. J Lond Math Soc, 1970, 2:323-329. |
| [6] | GOTO S, WATANABE K. On graded rings:I[J]. J Math Soc Japan, 1978, 30(30):179-213. |
| [7] | GOTO S, WATANABE K. On graded rings: II[J]. Tokyo J Math, 1978(1):237-261. |
| [8] | NASTASESEU C, OYSTAEYEN F V. Methods of graded rings[M]. New York: Springer, 2004. |
| [9] | ASENSIO M J, RAMOS J A L, TORRECILLAS B. FP-gr-injective modules and gr-FC-rings[J]. Algebra & Number Theory, 1999: 1-11. |
| [10] | NASTASESEU C, OYSTAEYEN F V. Graded ring theory [M]. New York: Springer, 1982. |
| [11] | YANG Xiaoyan, LIU Zhongkui. FP-gr-injective modules[J]. Math J Okayama Univ, 2011, 53:83-100. |
| [12] | 谢邦杰. 超穷数与超穷论法[M]. 长春: 吉林人民出版社, 1979. XIE Bangjie. Super poor number and super poor theory[M]. Changchun: Jilin Renmin Press, 1979. |
| [1] | 陈文静,刘仲奎. 关于n-强 Gorenstein FP-内射模的注记[J]. 山东大学学报（理学版）, 2014, 49(04): 50-54. |
|
||
