连通交换半环上三角矩阵代数的若当同构

Jordan Isomorphisms of Triangular Matrix Algebras over a Connected

利用若当同构的定义及其矩阵的性质,证明了如果R是含有恒等元1的2-非挠连通交换半环,Tn(R)是半环R上的三角矩阵代数,U是R上的任一代数,Φ:Tn(R)→U(n≥2)是若当同构,那么Φ或者是同构,或者是反同构.

Using the property of matrices and the definiens of Jordan isomorphism,we obtaint that every Jordan isomorphism of Tn（R） onto an arbitrary algebra,U over R is either an isomorphism or an anti-isomorphism,where R is a 2-torsionfree commutative semiring with identity 1,and Tn（R） is the algebra of all upper triangular n×n（n≥2） matrices over R,U is an arbitrary R-algebra.The result generalizes the previous results by Beidar K I.