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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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
PII: S 0002-9939(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