To pursue its civil fraud case against the American International Group's former chief executive, Maurice R. Greenberg, the New York attorney general’s office is taking an unusual step, the New York Times DealBook blog reported yesterday. It is giving up the right to contest Greenberg’s $115 million settlement of a separate class-action lawsuit—and the right to win up to $6 billion worth of cash damages in its own legal action—to help expedite a trial that would put the former AIG executive on the stand. In a letter to a state court judge sent yesterday, the office of Attorney General Eric T. Schneiderman wrote that it would continue to seek punishments against Greenberg, including a ban from the securities industry and a ban on serving as a director or officer of a publicly traded company.