Abstract :

We shall begin with examples of classes of maps for which injectivity implies surjectivity or surjectivity implies injectivity or otherwise and give a gentle introduction to the notion of surjunctivity. Then the concept of a trivolution with examples from algebras arising out of second duals of group algebras will be introduced. Next, we will give definitions and a few properties of multipliers and quotient rings of algebras. We will illustrate them for algebras of functions or operators.