Geodesic
Projective freeness and stable rank of algebras of complex-valued BV functions
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 844-853

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DOI

The paper investigates the algebraic properties of weakly inverse-closed complex Banach function algebras generated by functions of bounded variation on a finite interval. It is proved that such algebras have Bass stable rank 1 and are projective-free if they do not contain nontrivial idempotents. These properties are derived from a new result on the vanishing of the second Čech cohomology group of the polynomially convex hull of a continuum of a finite linear measure described by the classical H. Alexander theorem.
DOI : 10.4153/S000843952300005X
Mots-clés : Weakly inverse-closed Banach algebra, function of bounded variation, projective module, idempotent, stable rank, Hausdorff measure, continuum, Čech cohomology, covering dimension, polynomially convex hull 
Brudnyi, Alexander. Projective freeness and stable rank of algebras of complex-valued BV functions. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 844-853. doi: 10.4153/S000843952300005X
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     title = {Projective freeness and stable rank of algebras of complex-valued {BV} functions},
     journal = {Canadian mathematical bulletin},
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     year = {2023},
     volume = {66},
     number = {3},
     doi = {10.4153/S000843952300005X},
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