Polynomial Retracts

and the Jacobian Conjecture

Authors:
Vladimir Shpilrain and Jie-Tai Yu

Journal:
Trans. Amer. Math. Soc. **352** (2000), 477-484

MSC (1991):
Primary 13B25, 13P10; Secondary 14E09, 16S10

DOI:
https://doi.org/10.1090/S0002-9947-99-02251-5

Published electronically:
September 21, 1999

MathSciNet review:
1487631

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the polynomial algebra in two variables over a field of characteristic . A subalgebra of is called a retract if there is an idempotent homomorphism (a *retraction*, or *projection*) such that The presence of other, equivalent, definitions of retracts provides several different methods of studying and applying them, and brings together ideas from combinatorial algebra, homological algebra, and algebraic geometry. In this paper, we characterize all the retracts of up to an automorphism, and give several applications of this characterization, in particular, to the well-known Jacobian conjecture.

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Additional Information

**Vladimir Shpilrain**

Affiliation:
Department of Mathematics, The City College of New York, New York, New York 10031

Email:
shpil@groups.sci.ccny.cuny.edu

**Jie-Tai Yu**

Affiliation:
Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong

Email:
yujt@hkusua.hku.hk

DOI:
https://doi.org/10.1090/S0002-9947-99-02251-5

Received by editor(s):
March 11, 1997

Received by editor(s) in revised form:
August 20, 1997

Published electronically:
September 21, 1999

Additional Notes:
The second author’s research was partially supported by RGC Fundable Grant 344/024/0002

Article copyright:
© Copyright 1999
American Mathematical Society