ArticleOriginal scientific text
Title
Weak invertibility and strong spectrum
Authors 1
Affiliations
- Department of Mathematics and Computer Science, Georgia State University, Atlanta, Georgia 30303, U.S.A.
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.
Keywords
radical, norm, spectrum
Bibliography
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Pages:
255-269
Main language of publication
English
Received
1992-09-30
Published
1993
Exact and natural sciences