投射可迁环上矩阵环的若当同态(英文)

Jordan homomorphisms on matrix rings over projective-trivial ring

设R′是一个环,M_(n′)(R′)是R′上的n′×n′矩阵环.如果环R有不变基数性质并且每个有限生成的投射左R-模是自由模,则R是一个投射自由环.如果环R≌M_r(S),其中S是一个投射自由环,则R是一个投射可迁环.当R是一个投射可迁环时,给出了从M_(n′)(R′)到M_n(R)(n′≥n≥2)的若当同态的代数公式.

Let R’ be a ring and Mn’（R’） the n’ × n’ matrix ring over R’.A ring R is a projective-free ring if it has the invariant basis number property and every finitely generated projective left R-module is free.A ring R is a projectivetrivial ring if there is a projective-free ring S such that R（？）Mr（S）.When R is a projective-trivial ring,the algebraic formulas of Jordan homomorphisms from Mn’（R’） to Mn（R）（n’ ≥n≥ 2） are given.