Ad-nilpotent Elements of Semiprime Rings with Involution

作者：Lee Tsiu-Kwen^*

来源：Canadian Mathematical Bulletin, 2018, 61(2): 318-327.

DOI：10.4153/CMB-2017-005-3

• semiprime ring
• Lie algebra
• Jordan algebra
• faithful f-free
• involution
• skew (symmetric) element
• ad-nilpotent element
• Jordan element

Let R be an n!-torsion free semiprime ring with involution * and with extended centroid C, where n > 1 is a positive integer. We characterize a is an element of K, the Lie algebra of skew elements in R, satisfying (ad(a))(n) = 0 on K. This generalizes both Martindale and Miers' theorem and the theorem of Brox et al. In order to prove it we first prove that if a, b is an element of R satisfy (ad(a))(n) = ad(b) on R, where either n is even or b = 0, then (a - lambda)([(n+1)/2]) = 0 for some lambda is an element of C.

• 出版日期2018-6