Raymond Mortini (2014)
Annales Polonici Mathematici
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It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(𝔻̅). As a consequence, one obtains uniform closed subalgebras of A(𝔻̅) which have arbitrarily prescribed stable ranks.
Raymond Mortini (1992)
Studia Mathematica
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We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.
Joan Josep Carmona, Julià Cufí, Pere Menal (1992)
Publicacions Matemàtiques
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In this paper we prove a general result for the ring H(U) of the analytic functions on an open set U in the complex plane which implies that H(U) has not unit-1-stable rank and that has some other interesting consequences. We prove also that in H(U) there are no totally reducible elements different from the zero function.
Rørdam, Mikael (1997)
Documenta Mathematica
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John T. Baldwin, Kitty Holland (2001)
Fundamenta Mathematicae
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This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and U-rank of the infinite rank ω-stable theories constructed by variants of Hrushovski's methods. Sample result: For every k < ω, there is an ω-stable expansion of any algebraically closed field which has Morley rank ω × k. We include a corrected proof of the lemma in [1] establishing that the generic model is ω-saturated in the rank 2 case.
Andrzej Skowroński (2001)
Colloquium Mathematicae
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We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.
Michael Pannenberg (1990)
Mathematica Scandinavica
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Røordam, Mikael (2001)
Documenta Mathematica
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Robert J. Archbold, Eberhard Kaniuth (2006)
Studia Mathematica
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Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
Goldberg, Moshe (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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John N. Mather (1969)
Publications Mathématiques de l'IHÉS
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Graham Allan (1998)
Studia Mathematica
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We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.
Richard H. Herman, L.N. Vaserstein (1984)
Inventiones mathematicae
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Marius Dadarlat, Terry A. Loring (1994)
Annales de l'institut Fourier
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G. Elliott extended the classification theory of -algebras to certain real rank zero inductive limits of subhomogeneous -algebras with one dimensional spectrum. We show that this class of -algebras is not closed under extensions. The relevant obstruction is related to the torsion subgroup of the -group. Perturbation and lifting results are provided for certain subhomogeneous -algebras.