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FIXED ELEMENTS OF NONINJECTIVE ENDOMORPHISMS OF POLYNOMIAL ALGEBRAS IN TWO VARIABLES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 2 / April 2017
- Published online by Cambridge University Press:
- 20 October 2016, pp. 209-213
- Print publication:
- April 2017
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- Article
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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.
The module structure of Solomon's descent algebra
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 72 / Issue 3 / June 2002
- Published online by Cambridge University Press:
- 09 April 2009, pp. 317-334
- Print publication:
- June 2002
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- Article
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