Sigma-maps on triangular algebras

Abstract

Triangular algebras were introduced by Chase in the early 1960s. He ended up with these structures in the course of his study of the asymmetric behavior of semi-hereditary rings. Since their introduction, triangular algebras have played an important role in the development of ring theory. In the middle/late 1990s, several authors undertook the study of derivations and related maps over some families of triangular algebras. Here, we will focus our attention on σ-biderivations and σ-commuting maps of triangular algebras (σ is an automorphism of the algebra). We will introduce and describe a new class of automorphisms of triangular algebras, and provide many classes of triangular algebras whose automorphisms can be determined