Automorphisms Of Strictly Upper Triangular Matrices Algebras Over A Commutative Algebra

Throughout this paper, we assume that R is an arbitrary commutative ring with identity and A is a commutative R -algebra with identity. Denote by Nn(A) the algebra of all the strictly upper triangular n×n matrices over A, where n is an integer greater than 1. We undertake a further investigation of automorphisms studied by [7](Y. A. Cao, J. T. Wang), [14](Kezlan T. P.) and [15](Z. W. Tan, etc). We first show the definitions of four kinds of automorphisms of R -algebra Nn(A), which we call standard automorphisms. The main results are as follows. For /; = 2, there exists a module endomorphism h of A such that ρ(aE12) = h(a)En , a∈ A , for n = 3 , there exist diagonal, ring and central automorph- ism ηD , ξg , μf such that ρ = ηD ·ξg·μf ; for n> 4, every auto-morphism p of Nn(A) can be expressed as a product of standard automorphisms.