Monday, July 8 2019
11:30 - 12:30

#### Let R be an associative ring. For any x, y ∈ R, as usual the symbols x ◦ yand [x, y] will denote the anti-commutator xy + yx and commutator xy − yx andcalled Jordan product and Lie product, respectively. Recall that a map f of aring R into itself is said to be additive if f (x + y) = f (x) + f (y) for all x, y ∈ R.An additive map d : R → R is called a derivation if d(xy) = d(x)y + xd(y) holdsfor all x, y ∈ R. An additive map d : R → R is called a Jordan derivation ifd(x2 ) = d(x)x + xd(x) holds for all x ∈ R. An additive map x → x∗ of R intoitself is called an involution if (i) (xy)∗ = y ∗ x∗ and (ii) (x∗ )∗ = x hold for allx, y ∈ R. A ring equipped with an involution is known as a ring with involutionor a ∗-ring. An additive map d : R → R is called a Jordan ∗-derivation ifd(x2 ) = d(x)x∗ + xd(x) holds for all x ∈ R.In this talk, I will review some recent results of myself and collaborationsin certain class rings involving these mappings. Moreover, some examples andcounter examples will be discussed for questions raised naturally.

Download as iCalendar

Done