Jordan isomorphisms of triangular matrix algebras over a connected commutative ring (Q1573673)

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