Decomposition of Jordan automorphisms of strictly triangular matrix algebra over local rings Original Research Article

Let Nn+1(R) be the algebra of all strictly upper triangular n + 1 by n + 1 matrices over a 2-torsionfree commutative local ring R with identity. In this paper, we prove that any Jordan automorphism of Nn+1(R) can be uniquely written as a product of a graph automorphism, a diagonal automorphism, an inner automorphism and a central automorphism for n greater-or-equal, slanted 3. In the cases n = 1, 2, we also give a decomposition for any Jordan automorphism of Nn+1(R) (1 less-than-or-equals, slant n less-than-or-equals, slant 2).