A cancellation conjecture for free associative algebras

Authors:
Vesselin Drensky and Jie-Tai Yu

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3391-3394

MSC (2000):
Primary 16S10; Secondary 13B10, 13F20, 14R10, 16W20

Published electronically:
May 22, 2008

MathSciNet review:
2415020

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Abstract | References | Similar Articles | Additional Information

Abstract: We develop a new method to deal with the Cancellation Conjecture of Zariski in different environments. We prove the conjecture for free associative algebras of rank two. We also produce a new proof of the conjecture for polynomial algebras of rank two over fields of zero characteristic.

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Additional Information

**Vesselin Drensky**

Affiliation:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

Email:
drensky@math.bas.bg

**Jie-Tai Yu**

Affiliation:
Department of Mathematics, The University of Hong Kong, Hong Kong SAR, China

Email:
yujt@hkucc.hku.hk, yujietai@yahoo.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09111-9

Keywords:
Cancellation Conjecture of Zariski,
algebras of rank two,
polynomial algebras,
free associative algebras,
centralizers,
Jacobians,
algebraic dependence

Received by editor(s):
June 9, 2006

Received by editor(s) in revised form:
July 14, 2006, and October 31, 2006

Published electronically:
May 22, 2008

Additional Notes:
The research of the first author was partially supported by the Grant MI-1503/2005 of the Bulgarian National Science Fund

The research of the second author was partially supported by an RGC-CERG Grant

Communicated by:
Birge Huisgen-Zimmermann

Article copyright:
© Copyright 2008
American Mathematical Society