A Note on the Prime Spectrums of Character Rings of Finite Groups  

作　　者：CHEN Gang FAN Yun YUAN Yua 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China [2]School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Huhei, China [3]School of Computer, Wuhan University, Wuhan 430072, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2006年第2期339-342,共4页武汉大学学报（自然科学英文版）

基　　金：SupportedbytheNationalBasicResearchProgram(973ProgramG1999075102)

摘　　要：Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R（G） be the character ring of G. The prime spectrum of the commutative ring S×Z R（G） iv denoted by Spec（S×Z R（G）） and set π={p｜p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π＇-group, or a finite Abelian group, the number of the connetted components of Spec（ S×Z R （G） ） coincides with the number of the π-regular classes in G,Let G be a finite group with order g and S be a subring of the algebraic number field which contains the integral extension over Z generated by a g-th primitive root co of unity, and R（G） be the character ring of G. The prime spectrum of the commutative ring S×Z R（G） iv denoted by Spec（S×Z R（G）） and set π={p｜p is a rational prime number such that p^-1 S}. We prove that when G is a regroup, a π＇-group, or a finite Abelian group, the number of the connetted components of Spec（ S×Z R （G） ） coincides with the number of the π-regular classes in G,

关 键 词：prime spectrums  connected components π-regular conjugacy classes 

分 类 号：O152.1[理学—数学]