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FIXED ELEMENTS OF NONINJECTIVE ENDOMORPHISMS OF POLYNOMIAL ALGEBRAS IN TWO VARIABLES

Part of: Rings and algebras with additional structure Ring extensions and related topics

Published online by Cambridge University Press:  20 October 2016

YUEYUE LI  and
JIE-TAI YU
YUEYUE LI*
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, China email yylihi@outlook.com
JIE-TAI YU
Affiliation:
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China email jietaiyu@szu.edu.cn
*
✉yylihi@outlook.com
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Abstract

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Let $A_{2}$ be a free associative algebra or polynomial algebra of rank two over a field of characteristic zero. The main results of this paper are the classification of noninjective endomorphisms of $A_{2}$ and an algorithm to determine whether a given noninjective endomorphism of $A_{2}$ has a nontrivial fixed element for a polynomial algebra. The algorithm for a free associative algebra of rank two is valid whenever an element is given and the subalgebra generated by this element contains the image of the given noninjective endomorphism.

Keywords

fixed elementfree associative algebrapolynomial algebraretract

MSC classification

Primary: 13B10: Morphisms
Secondary: 16W20: Automorphisms and endomorphisms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 2 , April 2017 , pp. 209 - 213
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

The research of Yueyue Li was supported by NSF of China (Grant No. 11371165).

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