Jordan division algebras

Algebraic conditions on rings with involution

We are given a semiprime ring R with involution *. We show that the following conditions are equivalent. Condition 1: For each element x of R, [x*, x](=x*x − xx*) = 0. Condition 2: There is a fixed natural number N′ such that [x*, xN′] = 0, all elements x of R. Condition 3: There is a fixed natural number N such that for each element x of R, , where dx is the inner derivation induced by x, and is the Nth power of dx under composition of maps.

Involution Satisfying an Engel 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 no...

Involution satisfying a local Engel or power commuting condition

Structure of a certain class of rings with involution

/pdf/a-generalization-of-a-theorem-of-kaplansky-and-rings-with-1x4ut59010.pdf

A generalization of a theorem of Kaplansky and rings with involution.

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A generalization of a theorem of Kaplansky and rings with involution.