Certain invariant multiplicative subset of a simple Artinian ring with involution. II.

In the first part of the paper, we provide a fairly complete description of a simple ring R with involution f such that relative to f the traces of all elements of R form a commutative subset of R. This description is based on the characteristic of R. While the case of characteristic not 2 readily follows from current results in the literature, by contrast, the opposite case of characteristic 2 requires markedly more work. In the rest of the paper, the results carried out earlier are put to work to delineate the structure of a simple Artinian ring R with involution f, which is equipped with a given non central multiplicative subset M stabilized by f and preserved by all inner automorphisms of R, and such that the traces relative to f of all elements of M form a commutative subset of R. [ABSTRACT FROM AUTHOR]