Structures algébriques dans des anneaux fonctionnels

Abstract : In this thesis, we are interested in various problems of algebraic structures of some functional rings, in particular in the space H infinity of bounded analytic functions in the unit disc, in the Sarason algebra H infinity + C and in C(X,t)={fEC(X) : fot=f} with X compact Hausdorff space and t a topological involution on X. More precisely, we have characterized the finitely generated radical ideals in H infinity + C. Secondly, we have demonstrated that the absolute stable rank of C (X, t) coincides with Bass stable rank and topological stable rank. Finally, we are interested in the generalized corona problem in H infinity
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Jérôme Noël. Structures algébriques dans des anneaux fonctionnels. Mathématiques générales [math.GM]. Université de Lorraine, 2012. Français. ⟨NNT : 2012LORR0222⟩. ⟨tel-01749315⟩

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