WASHINGTON — The Supreme Court on Monday refused to review an appeals court’s determination that Apple had conspired with book publishers to raise the prices of digital books.

The court’s order, which following custom was issued without any accompanying explanation, puts into effect a $450 million settlement that Apple had agreed to pay if it lost the case. E-book buyers will receive $400 million in cash and credits and lawyers involved in the case will get $50 million.

The case arose from Apple’s 2010 entry into the e-book marketplace, which had been dominated by Amazon and its Kindle reader. Publishers frustrated with Amazon’s low prices welcomed the new retailer, its iPad device and its willingness to let them set their own prices, with Apple taking a cut of each sale.

Last year, a divided three-judge panel of the United States Court of Appeals for the Second Circuit, in New York, said the terms Apple had offered to five big publishers allowed them to engage in a price-fixing conspiracy.