On elements in algebras having finite number of conjugates

Details On elements in algebras having finite number of conjugates On elements in algebras having finite number of conjugates

2000-09-04

arxiv.org/abs/math/0009032v1

Publ. Math. Debrecen 57/ 1--2 (2000), 231--239

Mathematics

Rings and Algebras

8 pages, AMS-TeX

Scientific paper

Let $R$ be a ring with unity and $U(R)$ its group of units. Let $\Delta U=\{a\in U(R)\mid [U(R):C_{U(R)}(a)]<\infty\}$ be the $FC$-radical of $U(R)$ and let $\nabla(R)=\{a\in R\mid [U(R):C_{U(R)}(a)]<\infty\}$ be the $FC$-subring of $R$. An infinite subgroup $H$ of $U(R)$ is said to be an $\omega$-subgroup if the left annihilator of each nonzero Lie commmutator $[x,y]$ in $R$ contains only finite number of elements of the form $1-h$, where $x,y \in R$ and $h\in H$. In the case when $R$ is an algebra over a field $F$, and $U(R)$ contains an $\omega$-subgroup, we describe its $FC$-subalgebra and the $FC$-radical. This paper is an extension of [1].

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