Some properties of the Levitzki radical in alternative rings

Journal of the Australian Mathematical Society

Michael Rich¹ 

关键词: 17 D 05;   

DOI  :  10.1017/S1446788700024393

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Two local nilpotent properties of an associative or alternative ring A containing an idempotent are shown. First, if A = A11 + A10 + A01 + A00 is the Peirce decomposition of A relative to e then if a is associative or semiprime alternative and 3-torsion free then any locally nilpotent ideal B of Aii generates a locally nilpotent ideal 〈B〉 of A. As a consequence L(Aii) = Aii ∩ L(A) for the Levitzki radical L. Also bounds are given for the index of nilpotency of any finitely generated subring of 〈B〉. Second, if A(x) denotes a homotope of A then L(A) ⊆ L(A(x)) and, in particular, if A(x) is an isotope of A then L(A) = L(A(x)).

【 授权许可】

Unknown