Notes on cotorsion dimension of Hopf-Galois extensions

被引：0

作者：

Zhou, Xiaoyan ^{[1
]}

Wei, Min ^{[1
]}

机构：

[1] Nanjing Agr Univ, Coll Sci, Nanjing, Jiangsu, Peoples R China

来源：

TURKISH JOURNAL OF MATHEMATICS | 2016年 / 40卷 / 01期

关键词：

Hopf-Galois extension; cotorsion dimension; smash product; MODULES; ALGEBRAS; COVERS; RINGS;

D O I：

10.3906/mat-1408-59

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be a finite dimensional Hopf algebra over a field k and A/B be a right H-Galois extension. In this note the relationship of cotorsion dimensions between A and B will be studied. We prove that r.cot.D(A) <= r.cot.D(B) +1.D(H). Moreover, we give some sufficient conditions for which r.cot.D(A) = r.cot.D(B). As applications, we obtain some results about cotorsion dimension of the smash product.

引用

页码：108 / 113

页数：6

共 14 条

[1]

Caenepeel S, 2007, REV ROUM MATH PURES, V52, P151

[2]

Chase S.U., 1965, MEM AM MATH SOC, V58, P15

[3] Cotorsion dimensions and Hopf algebra actions [J].

Chen, Xiuli ;

Zhu, Haiyan ;

Li, Fang .

MATHEMATICAL NOTES, 2013, 93 (3-4) :616-623

[4]

DOI YK, 1990, ISRAEL J MATH, V72, P99, DOI 10.1007/BF02764613

[5] FLAT COVERS AND FLAT COTORSION MODULES [J].

ENOCHS, E .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 92 (02) :179-184

[6] HOPF-ALGEBRAS AND GALOIS EXTENSIONS OF AN ALGEBRA [J].

KREIMER, HF ;

TAKEUCHI, M .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) :675-692

[7] Global and finitistic dimension of Hopf-Galois extensions [J].

Liu, Ling ;

Guo, Qiao-Ling .

TURKISH JOURNAL OF MATHEMATICS, 2013, 37 (02) :210-217

[8]

Mao LX, 2006, MONOGR TXB PURE APPL, V249, P217

[9] Notes on cotorsion modules [J].

Mao, LX ;

Ding, NQ .

COMMUNICATIONS IN ALGEBRA, 2005, 33 (01) :349-360

[10]

Montgomery S., 1993, HOPF ALGEBRAS THEIR, V82

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