Jordan isomorphisms of triangular matrix algebras over a connected commutative ring Original Research Article

Let image be a 2-torsionfree commutative ring with identity 1, and let image, rgreater-or-equal, slanted2, be the algebra of all upper triangular r×r (rgreater-or-equal, slanted2) matrices over image. Then image contains no idempotents except 0 and 1 if and only if every Jordan isomorphism of image onto an arbitrary algebra over image is either an isomorphism or an anti-isomorphism.