Abstract
Let R be a ring with unity and U(R) its group of units. Let △U = {a ∈U(R) | [U(R) : CU(R)(a)] < ∞} be the FC-radical of U(R) and let ▽(R) = {a ∈ R | [U(R) : CU(R) (a)] < ∞} be the FC-subring of R. An infinite subgroup H of U(R) is said to be an w-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 ∈ R and h ∈ H. In the case when R is an algebra over a field F, and U(R) contains an w-subgroup, we describe its FC-subalgebra and the FC-radical. This paper is an extension of [1].
Original language | English |
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Pages (from-to) | 231-239 |
Number of pages | 9 |
Journal | Publicationes Mathematicae Debrecen |
Volume | 57 |
Issue number | 1-2 |
Publication status | Published - 2000 |
Externally published | Yes |
Keywords
- FC-elements
- Finite conjugacy
- Units
ASJC Scopus subject areas
- General Mathematics