Orbits in free algebras of rank two
作者:
Vesselin Drensky,
Jie Tai Yu,
期刊:
Communications in Algebra
(Taylor Available online 1998)
卷期:
Volume 26,
issue 6
页码: 1895-1906
ISSN:0092-7872
年代: 1998
DOI:10.1080/00927879808826246
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
LetFbe an algebra which is free in a class of algebras. In this paper we consider the following problem:If an endomorphism ψ ofFpreserves the orbit (AutF)(ω) of a nontrivial element ω ∈F, does this imply that ψ is an automorphism? We give positive solutions of this problem whenFis generated by two elements and is the free Lie algebra, free metabelian Lie algebra or free metabelian associative algebra, and ω is a certain kind of element.
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