强余挠模的忠实平坦余基变换

doi:10.6040/j.issn.1671-9352.0.2017.008

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (11): 92-94.doi: 10.6040/j.issn.1671-9352.0.2017.008

强余挠模的忠实平坦余基变换

王小青,梁力^*

兰州交通大学数理学院, 甘肃兰州 730070

收稿日期:2017-01-11 出版日期:2017-11-20 发布日期:2017-11-17
通讯作者: 梁力(1980— ),男,博士,副教授,研究方向为同调代数. E-mail:lliang@mail.lzjtu.cn E-mail:wxq647982@163.com
作者简介:王小青(1992— ),女,硕士研究生,研究方向为同调代数. E-mail:wxq647982@163.com
基金资助:
国家自然科学基金资助项目(11301240,11561039);甘肃省自然科学基金资助项目(1506RJZA075)

Strongly cotorsion modules under faithfully flat co-base change

WANG Xiao-qing, LIANG Li^*

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Received:2017-01-11 Online:2017-11-20 Published:2017-11-17

摘要/Abstract

摘要： 研究了强余挠模的忠实平坦余基变换。令R是环,S是忠实平坦R-代数,在一些额外的条件之下,证明了R-模G是强余挠的当且仅当Hom_R(S,G)是强余挠R-模且Ext^>0_R(S,G)=0;当且仅当Hom_R(S,G)是强余挠S-模且Ext^>0_R(S,G)=0。

关键词: 强余挠模, 忠实平坦余基变换, 余挠模

Abstract: Strongly cotorsion modules under faithfully flat co-base change are investigated. Let R be a commutative noetherian ring and S be a faithfully flat R-algebra. It is proved, under some extra assumptions, that an R-module G is strongly cotorsion if and only if HomR(S,G) is a strongly cotorsion R-module and Ext^>0R(S,G)=0 if and only if Hom_R(S,G) is a strongly cotorsion S-module and Ext^>0R(S,G)=0.

Key words: faithfully flat co-base change, strongly cotorsion module, cotorsion module

中图分类号:

O154.2

王小青,梁力. 强余挠模的忠实平坦余基变换[J]. 山东大学学报（理学版）, 2017, 52(11): 92-94.

WANG Xiao-qing, LIANG Li. Strongly cotorsion modules under faithfully flat co-base change[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 92-94.

参考文献

[1] XU Jinzhong. Flat covers of modules[M] // Lecture Notes in Mathematics, vol. 1634. New York: Springer-Verlag, 1996.
[2] YAN Hangyu. Strongly cotorsion(torsion-free)modules and cotorsion pairs[J]. Bulletin of the Korean Mathematical Society, 2010, 47: 1041-1052.
[3] HUANG Zhaoyong. Gorenstein injective and strongly cotorsion modules[J]. Israel Journal of Mathematics, 2013, 198: 215-228.
[4] ŠTOVÍCEK J. On purity and applications to coderived and singularity categories[J]. Preprint, arXiv: 1412. 1615.v1.
[5] CHRISTENSEN L W, KÖKSAL F, LIANG Li. Gorenstein dimensions of unbounded complexes and change of base(with an appendix by Driss Bennis)[J]. Science China(Mathematics), 2017, 60:401-420.
[6] ENOCHS E E, JENDA O M G. Relative homological algebra[M] // de Gruyter Expositions in Mathematics: vol. 30. Berlin: Walter de Gruyter Co, 2000.
[7] DING Nanqing, CHEN Jianlong. The flat dimension of injective modules[J]. Manuscripta Mathematica, 1993, 78:165-177.
[8] EMMANOUIL I, TALELLI O. On the at length of injective modules[J]. Journal of the London Mathematical Society, 2011, 84:408-432.
[9] AVRAMOV L L, FOXBY H B. Homological dimensions of unbounded complexes[J]. Journal of Pure and Applied Algebra, 1991, 71:129-155.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

强余挠模的忠实平坦余基变换

Strongly cotorsion modules under faithfully flat co-base change

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

多维度评价

本文评价

推荐阅读 0

[1]	杨鲜红,唐国亮,狄振兴. 三角矩阵环上Gorenstein平坦余挠模的黏合[J]. 《山东大学学报(理学版)》, 2023, 58(8): 18-25.
[2]	罗亚东,杨刚. Noetherian环上的Gorenstein余挠模[J]. 《山东大学学报(理学版)》, 2023, 58(8): 38-42.
[3]	王茜,沈磊,罗肖强. (m,n)-余挠模与(m,n)-平坦模[J]. 《山东大学学报(理学版)》, 2021, 56(1): 10-17.