# On Commutative and Non-Commutative C* -Algebras with the Approximate n-th Rott Property

- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- A. "Alex" Chigogidze, Professor and Department Chair (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/

**Abstract:** We say that a C *-algebra X has the approximate n-th root property (n = 2) if for every a ? X with kak = 1 and every " > 0 there exits b ? X such that kbk = 1 and ka - bnk < ". Some properties of commutative and non-commutative C *-algebras having the approximate nth root property are investigated. In particular, it is shown that there exists a non-commutative (resp., commutative) separable unital C *-algebra X such
that any other (commutative) separable unital C *-algebra is a quotient of X. Also we illustrate a commutative C *-algebra, each element of which has a square root such that its maximal ideal space has infinitely generated first ?Cech cohomology.

On Commutative and Non-Commutative C* -Algebras with the Approximate n-th Rott Property

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Created on 1/1/2005

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## Additional Information

- Publication
- arXiv:math/0503130v2 [math.OA] 7 Mar 2005
- Language: English
- Date: 2005
- Keywords
- C *-algebras with the approximate n-th root property, Rank of C *-algebras, Covering dimension, Invertible maps.

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