Involution satisfying a local Engel or power commuting condition
We are given a semiprime PI-ring R (i.e. R satisfies some polynomial identity) with *. It is to be shown that the following conditions are equivalent. Condition 1: Each element x of R is normal (i.e. (Formula presented.)). Condition 2: Associated to each element x of R is a natural number N = N(x) depending on x such that (Formula presented.) where dx maps each element y of R onto [y,x](= yx−xy) and (Formula presented.) is the Nth power of dx (under composition). Condition 3: * Associated to each element x of R is a natural number (Formula presented.) depending on x such that (Formula presented.).
|Keywords||Local Engel condition, local power commuting condition, ring with involution, semiprime ring|
|Journal||Communications in Algebra|
Chacron, M. (2017). Involution satisfying a local Engel or power commuting condition. Communications in Algebra, 45(5), 2018–2028. doi:10.1080/00927872.2016.1226879