# [1]张良云,刘应安.关于可分代数的Maschke定理[J].东南大学学报(自然科学版),1999,29(2):116-120.[doi:10.3969/j.issn.1001-0505.1999.02.022] 　Zhang Liangyun,Liu Yingan.Maschke’s Theorem of Separable Algebra[J].Journal of Southeast University (Natural Science Edition),1999,29(2):116-120.[doi:10.3969/j.issn.1001-0505.1999.02.022] 点击复制 关于可分代数的Maschke定理() 分享到： var jiathis_config = { data_track_clickback: true };

29

1999年第2期

116-120

1999-03-20

## 文章信息/Info

Title:
Maschke’s Theorem of Separable Algebra

1 南京农业大学理学院, 南京 210095)(2 南京林业大学,南京 210037
Author(s):
1 College of Science, Nanjing Agricultural University, Nanjing 210095
2 Nanjing Forestry University, Nanjing 210037

Keywords:

O153.3
DOI:
10.3969/j.issn.1001-0505.1999.02.022

Abstract:
This paper primarily gives the following conclusions: ① Let A be an algebra, thus C is a coseparable coalgebra if and only if A*C is a coseparable convolution coalgebra; ② Let A be a dimensional semisimple commutative Hopf algebra and B be a sub-Hopf algebra of A. if A is a coseparable coalgebra, then smash product #(A,B) is a separable algebra; ③ Let K〖FY1〗fHgπL be a split short exact sequence of Hopf algebras, thus H is a coseparable Hopf algebra if and only if K and L are coseparable Hopf algebras, also if H is a bi-separable Hopf algebra, then L is a bi-separable Hopf algebra.

## 参考文献/References:

[1] Doi Y.Homological coalgebra.J Math Soc Japan,1981,33(1):31～50
[2] Montgomery S.Hopf algebras and their actions on rings.Lectures in Math.Providenc AMS:CBMS LN 82,1993.1～238
[3] 张良云.可分代数和相关Hopf模.南京师范大学学报,1998,21(2):22～24
[4] 王栓宏.H-弱余模余代数和交叉余积.数学年刊,1995,16A(4):471～479
[5] Radford D E.Coreflexive coalgebras.J Alg,1973,26:512～535
[6] Cohen M.Hopf algebra actions.J Alg,1986,100:363～379
[7] Masuoka A.Generalization of cleft comodule algebras.Comm Alg,1992,20(12):3703～3721
[8] Koppinen M.Coideal subalgebras in Hopf algebrs:freeness,integrals,smash products.Comm Alg,1993,21(2):427～444
[9] 朱胜林.有限维半单余半单Hopf代数.Comm Alg,1993,21(11):3871～3885
[10] Cohen M.From supersymetry to quantum commutativity.J Alg,1994,168:1～27
[11] Molnar R K.Semi-direct products of Hopf algebras.J Alg,1977,47:29～51
[12] 李方,张良云.弱Hopf代数和半群环上的分式环.数学半年刊,1997,14(1):98～104