Jordan derivations and antiderivations on triangular matrices

Idempotence-preserving maps without the linearity and surjectivity assumptions

Idempotent elements determined matrix algebras

Over a 2-torsionfree commutative ring R with identity, the algebra of all strictly upper triangular n + 1 by n + 1 matrices is denoted by n 1. In this article, we prove that any Jordan automorphism of n 1 can be uniquely decomposed as a product of a graph automorphism, a diagonal automorphism, a central automorphism and an inner automorphism for n ≥ 3. In the cases n = 1, 2, we also give a decomposition for any Jordan automorphism of n 1.

Chong GuangCao

Papers

Modular automorphisms preserving idempotence and Jordan isomorphisms of triangular matrices over commutative rings