The basic tools for the investigation of different algebraic and analytical structures are representation and duality. “Representation” means that we establish a correspondence between our abstract structure and a similar, more particular one. Usually this more particular structure, the “representing” structure is formed by functions, defined on a set which is the so-called “dual” object. In order to get a “faithful” representation, it seems to be reasonable that the correspondence in question is one-to-one. Another reasonable requirement is that if the same procedure is applied to the dual object, then its dual can be identified with the original structure. In order to do that, the dual object should have an “internal” characterization. Finally, a characterization of the “representing” structure is also desirable : which functions on the dual object belong to the “representing” structure?
KeywordsMaximal Ideal Algebra Homomorphism Function Algebra Proper Ideal Dual Object
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