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A cancellation conjecture for free associative algebras
Author(s):
Vesselin
Drensky;
Jie-Tai
Yu
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3391-3394.
MSC (2000):
Primary 16S10;
Secondary 13B10, 13F20, 14R10, 16W20
Posted:
May 22, 2008
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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:
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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
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