Absolute stable rank and Witt cancellation for noncommutative rings

1988 ◽  
Vol 91 (3) ◽  
pp. 525-542 ◽  
Author(s):  
B. A. Magurn ◽  
W. Van der Kallen ◽  
L. N. Vaserstein
Keyword(s):  
Stable Rank ◽  
Noncommutative Rings

DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR MAPS

2021 ◽  
pp. 1-29
Author(s):  
ALEXANDER BRUDNYI
Keyword(s):  
Disjoint Union ◽  
A Priori ◽  
Holomorphic Functions ◽  
Stable Rank ◽  
Open Unit ◽  
Uniform Estimates ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Similar Approximation ◽  
Bounded Holomorphic

Abstract Let $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${\mathbb {D}}\subset {{\mathbb C}}$ . We show that the dense stable rank of $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^\infty ({\mathbb {D}})$ .

scholarly journals On the topological stable rank of non-selfadjoint operator algebras

2007 ◽  
Vol 341 (2) ◽  
pp. 239-253 ◽  
Author(s):  
K. R. Davidson ◽  
R. H. Levene ◽  
L. W. Marcoux ◽  
H. Radjavi
Keyword(s):  
Selfadjoint Operator ◽  
Operator Algebras ◽  
Stable Rank ◽  
Topological Stable Rank

scholarly journals HIGHER PRODUCT LEVELS OF NONCOMMUTATIVE RINGS

2001 ◽  
Vol 29 (1) ◽  
pp. 193-200 ◽  
Author(s):  
Jaka Cimprič
Keyword(s):  
Noncommutative Rings

scholarly journals The Cohen Macaulay Property for Noncommutative Rings

2017 ◽  
Vol 20 (6) ◽  
pp. 1433-1465 ◽  
Author(s):  
Ken A. Brown ◽  
Marjory J. Macleod
Keyword(s):  
Noncommutative Rings
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