Stable rank of holomorphic function algebras
Rudolf Rupp (1990)
Studia Mathematica
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Rudolf Rupp (1990)
Studia Mathematica
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Rørdam, Mikael (1997)
Documenta Mathematica
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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.
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.
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.
Røordam, Mikael (2001)
Documenta Mathematica
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Goldberg, Moshe (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Richard H. Herman, L.N. Vaserstein (1984)
Inventiones mathematicae
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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.
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.
Byunghan Kim, A. Pillay (2001)
Fundamenta Mathematicae
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We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.
Frank O. Wagner (2003)
Fundamenta Mathematicae
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A small profinite m-stable group has an open abelian subgroup of finite ℳ-rank and finite exponent.
John N. Mather (1969)
Publications Mathématiques de l'IHÉS
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Michael Pannenberg (1990)
Mathematica Scandinavica
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M. C. Laskowski, S. Shelah (2006)
Fundamenta Mathematicae
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We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.
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.
Maurice Kléman, Louise Michel (1978)
Recherche Coopérative sur Programme n°25
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