关于GI平坦模和GF挠模

doi:10.3969/j.issn.0253-2778.2015.03.003

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (3): 193-198.DOI: 10.3969/j.issn.0253-2778.2015.03.003

• 论著 • 上一篇

关于GI平坦模和GF挠模

王修建，赵玉娥，杜先能

1.皖西学院金融与数学学院，安徽六安 237012;2.青岛大学数学科学学院，山东青岛 266071; 3.安徽大学数学科学学院, 安徽合肥 230039

收稿日期:2013-02-05 修回日期:2014-03-03 接受日期:2014-03-03 出版日期:2014-03-03 发布日期:2014-03-03

On GI-flat and GF-torsion modules

WANG Xiujian, ZHAO Yue, DU Xianneng

1.School of Finance and Mathematics, West Anhui University, Luan 237012, China; 2.College of Mathematics, Qingdao University, Qingdao 266071, China; 3.School of Mathematical Sciences, Anhui University, Hefei 230039, China

Received:2013-02-05 Revised:2014-03-03 Accepted:2014-03-03 Online:2014-03-03 Published:2014-03-03
Contact: DU Xianneng
About author:WANG Xiujian, male, born in 1982, PhD/lecturer. Research field: ring and algebra representation. E-mail:xjwang@wxc.edu.cn
Supported by:
Supported by the Key Program of Excellent Youth Foundation of Higher Education in Anhui Province (2013SQRL071ZD), the National Natural Science Foundation of China (11126173).

摘要/Abstract

摘要： 研究了两类模：GI平坦模和GF挠模, 其中，GI表示Gorenstein内射模，GF表示Gorenstein平坦模；刻画了环的两个同调维数，即Gorenstein内射模的最大平坦维数和模的最大GF挠维数.同时也研究了这些模类和同调维数之间的关系.

关键词: Gorenstein内射模, Gorenstein平坦模, GI平坦模, GF挠模

Abstract: Two classes of modules were studied: GI-flat and GF-torsion modules, where GI stands for Gorenstein injective modules and GF for Gorenstein flat modules. Two homological dimensions for a ring were investigated, the supremum of the flat dimension of Gorenstein injective modules and the supremum of the GF-torsion dimension of all modules. The relation between these classes of modules and the homological dimensions was also studied.

Key words: Gorenstein injective modules, Gorenstein flat modules, GI-flat modules, GF-torsion modules

中图分类号:

王修建，赵玉娥，杜先能. 关于GI平坦模和GF挠模[J]. 中国科学技术大学学报, 2015, 45(3): 193-198.

WANG Xiujian, ZHAO Yue, DU Xianneng. On GI-flat and GF-torsion modules[J]. Journal of University of Science and Technology of China, 2015, 45(3): 193-198.

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关于GI平坦模和GF挠模

On GI-flat and GF-torsion modules

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