Two conjectures regarding the stability of ω-categorical theories
A. Lachlan (1974)
Fundamenta Mathematicae
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A. Lachlan (1974)
Fundamenta Mathematicae
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A. Lachlan (1980)
Fundamenta Mathematicae
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J. Wierzejewski (1976)
Fundamenta Mathematicae
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Bernard Aupetit, H. Mouton (1996)
Studia Mathematica
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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.
Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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A. Lachlan (1972)
Fundamenta Mathematicae
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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.
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.
Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.