12 江西师范大学学报（自然科学版） 2010年 Semigroup Algebras of Finite Type-A Semigroups CHEN Lin,GUO Xiao-jiang (Collge of Mathmatics and Infommatics Jiargxi Nomal Universiy,Nanchang Jiangxi 33022,China) Abstract:Semigroup algebras of finite type-A semigroups are studied by group representation theory.It is proved that semigoup algebras of finite type-A semigoups are isomorphic to direct sums of contracted semigroup algebras of finite weak Brandt semigroups.And it is obtained that semigoup algebras of finite type-A semigroups contain identities.These results extend the related results on semigroup algebras of finite inverse semigroups. Key words:semigoup algebras;type-A semigroup;weak Brandt semigroup;PA blocked Rees matrix semigroup (责任编辑：曾剑锋) (上接第7页) 当A=1时，根据柯西积分公式(2)有-1业=2方ie) =2i.当n>1时，由高阶导数公式(5) z=0 知=2ey =0 (n-1)! 参考文献： 【刂钟玉泉.复变函数论[M.北京：高等教育出版社.2004. [习余家荣.复变函数[M.北京：高等教育出版社，2000. 【习龚冬保.复变函数典型题[M.西安：西安交通大学出版社2002. 【杨丽。张伟伟.柯西积分公式的应用[】.沧州师范专科学校学报.2006,22(3：6467. 【了刚家泰谭欣欣.复变函数全程学习指导与解题能力训练[M.大连：大连理工大学出版社，2001 The Cauchy Integral Formula and Its Application in Integration YI Cai-feng,PAN Hengyi (Collge of Mathematics and Infommatics Jiangxi Nomal Universily.Nanchang Jiangxi 3322China) Abstract:It is expounded that the importance of Cauchy integral fomula in the theory of analytic function firstly,and it is described that the Cauchy integral fommula of various formal and the fommula of higher derivative,in the end,the applica- tion of these formula in integration is illustrationed by the example. Key words:analytic function;complex integral;Cauchy integral fommula (责任编辑：王金莲) ?1994-2018 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.netSemigroup Algebras of Finite Type-A Semigroups CHEN Lin , GUO Xiao-jiang (College of Mathematics and Informatics, Jiangxi Normal University , Nanchang Jiangxi 330022 ,China) Abstract:Semigroup algebras of finite type-A semigroups are studied by group representation theory .It is proved that semigroup algebras of finite type-A semigroups are isomorphic to direct sums of contracted semigroup algebras of finite weak Brandt semigroups .And it is obtained that semigroup algebras of finite type-A semigroups contain identities .These results extend the related results on semigroup algebras of finite inverse semigroups . Key words:semigroup algebras ;type-A semigroup ;weak Brandt semigroup ;PA blocked Rees matrix semigroup (责任编辑:曾剑锋) (上接第 7 页) 当 n =1 时,根据柯西积分公式(2)有∫|z|=1 e z z n dz =2πi(e z) z =0 =2πi .当 n >1 时, 由高阶导数公式(5) 知∫|z|=1 e z z n dz = 2πi (n -1)！ (e z)(n-1) z =0 = 2πi (n -1)！ . 参考文献 : [ 1] 钟玉泉.复变函数论 [ M] .北京:高等教育出版社, 2004 . [ 2] 余家荣.复变函数 [ M] .北京:高等教育出版社, 2000 . [ 3] 龚冬保.复变函数典型题 [ M] .西安:西安交通大学出版社, 2002 . [ 4] 杨丽, 张伟伟.柯西积分公式的应用 [ J] .沧州师范专科学校学报, 2006 , 22(3):64-67. [ 5] 刚家泰, 谭欣欣.复变函数全程学习指导与解题能力训练 [ M] .大连:大连理工大学出版社, 2001 . The Cauchy Integral Formula and Its Application in Integration YI Cai-feng , PAN Heng-yi (College of Mathematics and Informatics, Jiangxi Normal University , Nanchang Jiangxi 330022 ,China) Abstract :It is expounded that the importance of Cauchy integral formula in the theory of analytic function firstly , and it is described that the Cauchy integral formula of various formal and the formula of higher derivative , in the end , the applica￾tion of these formula in integration is illustrationed by the example. Key words:analytic function ;complex integral ;Cauchy integral formula (责任编辑:王金莲) 12 江西师范大学学报(自然科学版) 2010 年