C-投射(内射,平坦)模与优越扩张

doi:10.6040/j.issn.1671-9352.0.2016.386

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (8): 85-89.doi: 10.6040/j.issn.1671-9352.0.2016.386

C-投射(内射,平坦)模与优越扩张

陈秀丽¹,陈建龙²

1. 浙江水利水电学院基础部, 浙江杭州 310018;2. 东南大学数学系, 江苏南京 210096

收稿日期:2016-08-22 出版日期:2017-08-20 发布日期:2017-08-03
作者简介:陈秀丽(1980— ),女,博士,讲师,研究方向为Hopf代数、同调代数及代数表示论的研究. E-mail:xiulichen1021@126.com
基金资助:
国家自然科学基金资助项目(11371089;61573322)

Homological dimensions with respect to semidualizing modules and excellent extensions

CHEN Xiu-li¹, CHEN Jian-long²

1. Department of Basic Courses, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, Zhejiang, China;
2. Department of Mathematics, Southeast University, Nanjing 210096, Jiangsu, China

Received:2016-08-22 Online:2017-08-20 Published:2017-08-03

摘要/Abstract

摘要： 令C作为R-模为半对偶模,其中R为交换环。在(几乎)优越扩张的条件下研究了与半对偶模C相关模类的传递性,讨论了C-投射,内射及平坦预盖及预包的相关性质。作为应用,证明了当环扩张S≥R为优越扩张时,R为诺特环当且仅当S为诺特环;R为凝聚环当且仅当S为凝聚环。

关键词: 优越扩张, 平坦)模, 凝聚环, 半对偶模, C-投射(内射, 诺特环

Abstract: Let C be a semidualizing R-module with R being a commutative ring. It is investigated the transfer properties of C-homological dimensions under(almost)excellent extensions, and it is discussed that the precovering and preenveloping properties of the C-projectives, C-injectives, and C-flats. As applications, it is proved that if S≥R is an excellent extension, then R is Noetherian if and only if S is Noetherian, and R is coherent if and only if S is coherent.

Key words: C-homological dimensions, coherent ring, Noetherian ring, semidualizing module, excellent extension

中图分类号:

O153.3

陈秀丽,陈建龙. C-投射(内射,平坦)模与优越扩张[J]. 山东大学学报（理学版）, 2017, 52(8): 85-89.

CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89.

参考文献

[1] SATHER-WAGSTAFF S, SHARIF T, WHITE D. AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules[J]. Algebra Represent Theory, 2011, 14(3):403-428.
[2] SATHER-WAGSTAFF S, SHARIF T, WHITE D. Tate cohomology with respect to semidualizing modules[J]. J Algebra, 2010, 324:2336-2368.
[3] BONAMI L. On the structure of skew group rings[M] //Algebra Berichte, 48. Munich: Verlag Reinhard Fischer, 1984.
[4] XUE Weimin. On almost excellent extensions[J]. Algebra Colloq, 1996(3):125-134.
[5] CHRISTENSEN L W. Semi-dualizing complexes and their Auslander categories [J]. Trans Amer Math Soc, 2001, 353:1839-1883.
[6] LIU Zhongkui. Excellent extensions and homological dimensions [J]. Comm Algebra, 1994, 22:1741-1745.
[7] HUANG Zhaoyong, SUN Juxiang. Invariant properties of representations under excellent extensions [J]. J Algebra, 2012, 358(3): 87-101.
[8] WANG Dingguo. Modules with flat socles and almost excellent extensions[J]. Acta Math Vietnam, 1996, 21(2): 295-301.
[9] WHITE D. Gorenstein projective dimension with respect to a semidualizing module[J]. J Commut Algebra, 2010, 2(1):111-137.
[10] HOLM H, WHITE D. Foxby equivalence over associative rings [J]. J Math Kyoto Univ, 2007, 47(4): 781-808.
[11] JORGENSEN D A, LEUSCHKE G J, SATHER-WAGSTAFF S. Presentations of rings with nontrivial semidualizing modules[J]. Collect Math, 2012, 63: 165-180.
[12] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Berlin: Walter de Gruyter, 2000.
[13] CHEN Xiuli, CHEN Jianlong. Cotorsion dimensions relative to semidualizing modules[J]. J Algebra Appl, 2016, 15(6):16501041-165010414.
[14] FANG Hongjin. Normalizing extensions and modules[J]. J Math Res Exp, 1992, 12(3): 401-406.
[15] ZHANG Dongdong, OUYANG Baiyu. Semidualizing modules and related modules[J]. J Algebra Appl, 2011, 10(6):1261-1282.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

C-投射(内射,平坦)模与优越扩张

Homological dimensions with respect to semidualizing modules and excellent extensions

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]	郭寿桃,王占平. 正合零因子下模的Gorenstein同调维数[J]. 山东大学学报（理学版）, 2018, 53(10): 17-21.
[2]	郭莹, 姚海楼. 多项式环的表现维数[J]. 山东大学学报（理学版）, 2015, 50(04): 71-75.
[3]	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.