On Elements in Algebras Having Finite Number of Conjugates
نویسنده
چکیده
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 ω-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 ω-subgroup, we describe its FC-subalgebra and the FC-radical. This paper is an extension of [1].
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تاریخ انتشار 2000