Washington ? Elinor Ostrom, 76, known for her work on the management of common resources, is the first woman to win a Nobel in economics. She shares this year’s prize with fellow American Oliver Williamson, 77, who pioneered the study of how and why companies structure themselves and how they resolve conflicts.

Monday’s final prizes of 2009 capped a year in which a record five women won Nobels. And it was an exceptionally strong year for the United States, too. Eleven U.S. citizens, some with dual nationality, were among the 13 Nobel winners, including President Barack Obama, who won the Nobel Peace Prize on Friday.

In other awards, Americans Elizabeth H. Blackburn, Carol W. Greider and Jack W. Szostak shared the prize in medicine for discovering a key mechanism in the genetic operations of cells, an insight that has inspired new lines of research into cancer.

The physics prize was split between Americans Charles K. Kao, who helped develop fiber-optic cable, and Willard S. Boyle and George E. Smith, who invented the “eye” in digital cameras.

Americans Venkatraman Ramakrishnan and Thomas Steitz and Ada Yonath of Israel shared the chemistry prize for their atom-by-atom description of ribosomes.