环上带有广义导子和自同构的恒等式(英文)  

Identities With Generalized Derivations and Automorphisms on Rings

作　　者：魏丰[1] 肖占魁[1] 

机构地区：[1]北京理工大学应用数学系,北京100081

出　　处：《数学进展》2009年第1期57-68,共12页Advances in Mathematics（China）

基　　金：supported by a research fellowship from the China Scholarship Council and the Basic Research Foundation of Beijing Institute of Technology.

摘　　要：设R是一个素环,R_F是它的左Martindale商环.如果φ(x_i^(g_(ik)Δ_(ij)))是环R的某个本质理想I的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(z_(ikj))是环R_F的一个广义多项式恒等式.设R是一个具有特征p(?)0的半素环,R_F是它的左Martindale商环.如果φ(x_i^(g_(ik)Δ_(ij)f_(ik)))是环R的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(z_(ikj)f_(ik)e(Δ_(ij)))是环R_F的一个广义多项式恒等式,这里f_(ik)和e(Δ_(ij))是RF中的幂等元.Let R be a prime ring and RF be its left Martindale quotient ring. If φ（xigik△ij） is a multilinear reduced generalized differential identity with automorphisms for an essential ideal I of R, then φ（Zikj） is a generalized polynomial identity for RE. Let R be a semiprime ring with characteristic p ≥ 0 and RF be its left Martindale quotient ring. If φ（xigik△ij） is a multilinear reduced generalized differential identity with automorphisms for R, then φ（zikjfike△ij）） is a generalized polynomial identity for RE, where fik and e（△ij） are idempotents in the center of RF.

关 键 词：恒等式 广义导子 自同构 (半)素环 

分 类 号：O153.3[理学—数学]