Publishing house / Journals and Serials / Studia Mathematica / All issues

Abstract

A notion of weak invertibility in a unital associative algebra A and a corresponding notion of strong spectrum of an element of A is defined. It is shown that many relationships between the Jacobson radical, the group of invertibles and the spectrum have analogues relating the strong radical, the set of weakly invertible elements and the strong spectrum. The nonunital case is also discussed. A characterization is given of all (submultiplicative) norms on A in which every modular maximal ideal M ⊆ A is closed.