关联代数上的(m,n)-Jordan导子和(m,n)导子  

(m,n)-Jordan derivations and(m,n)derivations on incidence algebras

作　　者：周斯名 袁鹤[1] ZHOU Siming;YUAN He(School of Mathematics,Jilin Normal University,Changchun Jilin 130000)

机构地区：[1]吉林师范大学数学学院,吉林长春130000

出　　处：《宁夏师范学院学报》2022年第7期5-10,共6页Journal of Ningxia Normal University

摘　　要：设(X,≤)是一个有限预序集,R是含单位元的|(m+n)(m-n)|-扭自由的交换环.设I(X,R)是定义在R上的关于X的关联代数.φ,∅:I(X,R)→I(X,R)是线性映射,证明了对任意A∈I(X,R),满足(m+n)φ(A^(2))=2mAφ(A)+2nφ(A)A,则φ恒等于零及对任意A,B∈I(X,R),满足m∅(AB)+n∅(BA)=mA∅(B)+m∅(A)B+n∅(B)A+nB∅(A),则∅是导子.Let(X,≤)be a finite pre-ordered set and R be a|(m+n)(m-n)|-torsion free commutative ring with the identity.Suppose that I(X,R)is the incidence algebra of X over R.φand∅are linear maps from I(X,R)to I(X,R).We prove that φ is equal to zero when(m+n)φ(A^(2))=2mAφ(A)+2nφ(A)A holds for any A∈I(X,R)and∅is a derivation when m∅(AB)+n∅(BA)=mA∅(B)+m∅(A)B+n∅(B)A+nB∅(A)holds for any A、B∈I(X,R).

关 键 词：关联代数 (m n)-Jordan导子 (m n)导子 

分 类 号：O152.5[理学—数学]