Atlantic Richfield Co. announced that it is considering selling stock in its Lyondell Petrochemical Co. subsidiary to the public while retaining a controlling interest in the Texas firm. Arco’s board ordered a study of the plan and hasn’t decided definitely whether to make the public offering, the Los Angeles-based company said. Lyondell produces petrochemicals in Channelview, Tex., and has an oil refinery in Houston. If the stock offering proceeds, Arco would sell about 50% of Lyondell and retain slightly less than half the stock, the company said. Money raised through the sale would be used for general corporate purposes at Arco, including expanding a stock repurchase program.