On Jordan and Jordan*-Generalized Derivations in Semiprime Rings with Involution
The purpose of this note is to prove the following result. Let R be a6 −torsion free semiprime *-ring and let G: R−→R be an additive mapping such that G(xyx )= G(x)y ∗ x ∗ + xD(y)x ∗ + xyD(x) holds for all x,y ∈ R and some *-derivations D of R. Then G is a Jordan*generalized derivation.
Jordan derivations of prime rings
1. Given any associative ring A one can construct from its operations and elements a new ring, the Jordan ring of A, by defining the product in this ring to be a o b=ab+ba for all a, bEA, where the product ab signifies the product of a and b in the associative ring A itself. If R is any ring, associative or otherwise, by a derivation of R we shall mean a function, ', mapping R into itself so that
Same-Sex Marriage in the United States
This Chapter gives a brief analysis of the status of same-sex marriage in the United States prior to the US Supreme Court decisions of 2013 and the status of litigation and political reforms triggered in part by these court decisions. It shows that marriage is a central institution in the country’s rationale of family law in ways that separate it from other western countries that have allowed same-sex marriage.