半群S—分次模范畴的同态集与冲积R＃S^＊的分次Jacobson根  

The Sets of Morphisms for Gategories of Semigroup-graded Modules and the Graded Jacobson Radicals of Smash Product R # S *

作　　者：蔡炳苓[1] 刘稳[1] 刘淑霞[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050016

出　　处：《河北师范大学学报（自然科学版）》2003年第2期130-133,共4页Journal of Hebei Normal University：Natural Science

基　　金：河北省自然科学基金资助项目 ( 10 2 132 )

摘　　要：对于任意半群S ,证明了半群分次模范畴Rgr的 1个结果 :在一定条件下 ,HOMR(M ,N) =HomR(M ,N) (其中HOM R(M ,N)是从M到N的所有s(s∈S)次分次同态作成的群 ,HomR(M ,N)是从M到N的所有R模同态作成的群 ,M ,N∈R gr ,M∈RMod) ,推广了群分次环与模的相应结果 .对任意半群的冲积R #S ,讨论了当R有 1且S为右可消幺半群时 ,R #S 与其分量子环Re 的理想间的关系 ;并证明了当S为左可消幺半群时 ,R #S 的J根与R的分次J根之间的关系 :J(R #S ) JS(R) #S ,其中JS(R)为R的所有弱拟正则分次左理想的和 .Let S denote a semigroup and R is a Sgraded ring.A result of Rgr(the category of semigroupgraded modules)satisfying certain conditions is proved,i.e.HOM R(M,N)=Hom R( M, N)(HOM R)(M,N)is a group of all graded morphisms of degree s(s∈S)from M to N,Hom R( M, N)is for the R-modules morphisms from M to N,M,N∈Rgr, M∈RMod),which generalizes the corresponding results of rings and modules graded by a group G.Then,the corresponding relations between ideals of the smash product R#S* and ideals of the identity component R e for R with 1 and S which is right cancellative is build;and the relation between Jradical of R#S* and graded Jradical of R when S is left cancellative is proved,i.e.J(R#S*)J S(R)#R*(J S(R)is the sum of all weakly quasi-regular ideals of R).

关 键 词：半群S-分次模范畴 同态集 冲积R#S^＊ 分次JACOBSON根 S-分次环 可消幺半群 分次同态 

分 类 号：O153.3[理学—数学]