Displaying similar documents to “Constructing ω-stable structures: Computing rank”

Stable rank and real rank of compact transformation group C*-algebras

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.

On the unit-1-stable rank of rings of analytic functions.

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.

Small profinite m-stable groups

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.

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that rank ( P * A Q ) = rank ( P * A ) + rank ( A Q ) - rank ( A ) , where A is idempotent, [ P , Q ] has full row rank and P * Q = 0 . Some applications of the rank formula to generalized inverses of matrices are also presented.