When the UCLA School of Law announced a $10 million gift from Lowell Milken to establish a business law institute in his name earlier this month, the university described him as a “pioneer in education reform” and a “leading philanthropist.”

Behind the scenes, Mr. Milken’s big donation has set off an internal debate at the school. While many faculty members welcomed the money, one of the University of California, Los Angeles’s top business law professors has said the gift poses deep ethical problems and reputational risks, given Mr. Milken’s run-in with securities regulators two decades ago.

“The creation of a Lowell Milken Institute for Business Law and Policy will damage my personal and professional reputation, as I have devoted my career to arguing for investor protection and honest and ethical behavior in business,” Lynn A. Stout wrote in a letter last month to the president of the University of California and UCLA’s chancellor.

Ms. Stout, a specialist in corporate governance and moral behavior, said in an interview last week, “I think it’s somewhat distressing that so few people seem to be aware of Lowell and Michael Milken’s business history.”

The Milken name is still a lightning rod on Wall Street and in legal circles. Michael Milken and his younger brother, Lowell, were central figures in creating the booming junk-bond market of the 1980s and the subsequent collapse of the investment bank where they worked, Drexel Burnham Lambert.

In a controversial deal with the government, Michael pleaded guilty to securities law violations after the government agreed to drop criminal charges against Lowell. Michael served a 22-month prison term and paid $600 million in fines and restitution.

As part of a settlement in a related civil matter, the Securities and Exchange Commission permanently barred the two brothers from the securities industry.

Lowell Milken did not admit to any wrongdoing.

Kenneth W. Graham Jr., a retired UCLA law professor, said it was a mistake to take the gift from Mr. Milken, a 1973 graduate of the school and longtime donor to it. “To say that I was outraged would be something of an understatement,” wrote Mr. Graham in an e-mail.

But other UCLA law professors disagree with the objections and are thrilled with Mr. Milken’s largess. Since their legal woes, the Milken brothers have become prominent philanthropists, donating hundreds of millions of dollars to a variety of causes, most notably in the areas of medical research and education.

“Save for one dissident professor, the entire business law faculty is grateful for this gift,” Kenneth N. Klee, a bankruptcy law scholar, said.

The current debate surrounding Lowell Milken’s gift highlights the quandary that public universities across the country face as the fiscal woes of states have forced them to look increasingly to private corporations and wealthy alumni for financial support. Law schools are typically among a state school’s most profitable graduate programs.

“We’re staring down the barrel of another round of cuts in California and relying on alumni giving is essential for us to be able to provide a quality education,” said Stephen Bainbridge, a U.C.L.A. corporate law professor. “If it wasn’t for these sorts of gifts we’d have even tighter budgetary constraints.”

When asked to respond to complaints about Mr. Milken’s gift, Bonnie Somers, a spokeswoman for the Milken Family Foundation, issued a written statement.

“Basic fairness requires that individuals be evaluated solely on the basis of their own conduct and Lowell Milken’s life of accomplishment and service speaks for itself,” her statement said. She added that the foundation respected the fact that U.C.L.A. “understands that in the United States of America, its citizens are presumed innocent until proven otherwise.”

Lauri Gavel, a law school spokeswoman, also issued a written statement: “Only one member of the business law faculty has expressed anything less than gratitude — and that concern was surprising, given that this professor was involved early in the process, has been a beneficiary of the donor’s philanthropy, and did not raise objections until quite recently.”

This is not the first time a Milken has generated controversy at UCLA In 1994, the university severed its ties with an education company controlled by Michael R. Milken that planned to sell videotapes of a lecture series he gave at the school. The company agreed to remove any identification of UCLA from the tapes after the school said it received many complaints from state officials who did not want the university’s name associated with Mr. Milken.

While Lowell Milken’s gift was the capstone of the law school’s $100 million fund-raising campaign, several other benefactors made donations and in return had buildings, conference rooms, professorships and scholarship funds named in their honor.

Mr. Milken is not the only leading donor in the current campaign that has tussled with regulatory authorities. The capital drive also led to the creation of the Stewart and Lynda Resnick Endowed Fund in Support of Public Interest Law. The Resnicks are the Beverly Hills beverage industry entrepreneurs who own Fiji Water and Pom Wonderful.

Last fall, the Federal Trade Commission filed a civil lawsuit against the Resnicks, accusing them and their company, Pom Wonderful, of making “false and unsubstantiated claims” that their pomegranate juice product helped reduce the risk of heart disease and erectile dysfunction.

Jill Gottesman, a spokeswoman for Pom Wonderful and the Resnicks, which are fighting the charges, has called the government’s allegations “completely unwarranted.”

Law professors unaffiliated with UCLA say that even though the economic environment makes it challenging for public schools to finance vital programs, they need to consider the potential risks in accepting private money. Thane Rosenbaum, a law professor at Fordham University, said that UCLA’s gifts from Mr. Milken and the Resnicks reflect a kind of “academic cynicism.”

“Here is a major law school, with state funding in California deteriorating, now taking its money from people engaged in questionable behavior,” said Mr. Rosenbaum. “It’s unbecoming to a great university.”

Other schools have in the past refused money, or taken other actions, when their benefactors have become involved in corporate wrongdoing. In the 1980s, Princeton returned money from Ivan Boesky to build a Jewish Center after the government charged the Wall Street financier with insider trading crimes. Seton Hall removed the name of L. Dennis Kozlowski from an academic building in 2005, after the conviction of the former Tyco chief executive for looting his company.

Inside the halls of UCLA, the protests of Ms. Stout, a tenured professor whose most recent book is “Cultivating Conscience: How Good Laws Make Good People,” has caused consternation among her colleagues.

Mr. Bainbridge, the corporate law professor, said that though he considered Ms. Stout a friend, he disagreed with her position.

“I believe that Lynn genuinely thinks that this hurts the school by giving Milken the UCLA imprimatur of being a good guy and an ethical person,” said Mr. Bainbridge.

“I think it’s unfortunate that we’re dragging up stuff that happened a quarter of a century ago — and for which any debt to society has long been paid — to taint something that is going to help our students tremendously.”