Automorphisms Of Formal Triangular Matrix Rings

Throughout this paper, we assume that A and B are rings with identities and the only idempotents in A and B are 1 and 0. Let M is a nonzero left A right B bimodule. Theformat triangular matrix ring Tri(A,M,B) has as itselements format matrices where a∈A, b∈B and m∈M.We undertake a further investigation of auto-morphisms on upper triangular matrices studied by Wai-shun Cheung ([16]), A. Haghang and K. Varadardjan ([1]), You' an Cao ([5]) andLeping Xie. etc ([18]). The main result of this paper is as follows: assume A,B and Mare defined above, the map φ on Tri(A,M,B) is an automorphism if and only if there are an automorphism g of A , an automorphism h of B , a (g,h)-semi linear automorphism k of M and an element d of Msuch that...