Modular automorphisms preserving idempotence and Jordan isomorphisms of triangular matrices over commutative rings Original Research Article

Suppose image is a commutative ring with 1 and 2 being the units of image . Let image be the n×n upper triangular matrix modular over image , and let image be the set of all image -module automorphisms on image that preserve idempotence. The main result in this paper is that image if and only if there exist an invertible matrix image and an idempotence image such that f(X)=U(eX+(1−e)Xδ)U−1 for any image , where Xδ=(xn+1−jn+1−i). As applications, we determine all Jordan isomomorphisms of image over the ring image