A day after giving state governments broad new protections against lawsuits, the Supreme Court said yesterday that it will decide next term whether people can sue a state they accuse of cheating the federal government. The justices said they will hear Vermont's argument that the Constitution bars such lawsuits against states under the federal False Claims Act.

In a separate case yesterday, the court set aside a ruling that let bankrupt debtors sue the state agencies that try to collect from them. The justices told a federal appeals court to reexamine its ruling in a Georgia case that would have allowed such lawsuits when the debtors allege that a state agency violated their federally protected civil rights.

On Wednesday, the last regular day of the term, the justices broadened the "sovereign immunity" states enjoy against lawsuits by businesses and private citizens in federal and state courts and enhanced the states' power in relation to the federal government.

The justices also issued orders in dozens of remaining appeals yesterday. The court allowed the federal government to ban prisoners from getting Playboy, Penthouse and other sexually explicit publications and without any comment or dissent rejected an appeal by three inmates, Playboy Enterprises Inc., the publisher of Penthouse magazine and a publishing trade organization in a free-speech challenge to the ban.

The justices let stand a federal appeals court ruling that the Bureau of Prisons may enforce legislation adopted by Congress in 1996 requiring wardens to stop the distribution of any material that is "sexually explicit or features nudity."