David Begelman, whose admitted financial improprieties have divided the film colony and triggered a spate of Hollywood scandal stories, resigned yesterday as president of the motion picture and television division fo Columbia Pictures Industries Inc.

The announcement, released at the company's New York headquarters, said that Columbia and Begelman were negotiating a settlement of his contract, which had more than a year to run. It paid him about $400,000 last year in salary and benefits.

Alan Hirschfield, president of the parent company, said there were also were discussions about engaging [Begelman] solely as an independent producer."

Begelman's resignation was credited for a rise yesterday of $1.50 a share in Columbia stock, which is traded on the New York Stock Exchange. Late last year, the stock hit about $20 a share on the success of Columbia's blockbuster, "Close Encounters of the Third Kind," but it had sunk below $14 after Begelman's reinstatement was announced in mid December. It closed yesterday at $16.75.

There was another major development in the movie business yesterday. Arthur Krim, the former chairman of United Artists, and four other movie executives who joined him recently in resigning from UA, announced formation of a production company under the aegis of Warner Brothers. With about $90 million in initial financing, the still-unnamed entity becomes the largest independent production company in Hollywood.

United Artists under Krim's management has been the most successful film company in Hollywood. In 1977, UA worldwide films rentals totaled $318 million with such box-office hits as "Rocky," "Annie Hall" and "Semi-Tough." Krim and the others said they quit because of friction with UA's parent, the conglomerate Transamerica Corp.

The Begelman affair began last spring when a clerk at the studio's accounting department sent a tax form to actor Cliff Robertson for $10,000 allegedly paid him by the company for work in 1976. Robertson, who had not worked for Columbia that year, eventually informed the FBI and local authorities about the apparent embezzlement after his accountant learned that Begelman had cashed the $10,000 check at a Beverly Hills branch of the Wells Fargo Bank.

Begelman was suspended for 2 1/2 months while Columbia conducted an internal investigation. It concluded the executive had obtained by "improper means" more than $60,000 from the company by cashing checks made out to Robertson and director Martin Ritt, among others.

The invesigation also concluded that Begelman had padded his expense account by $23,200. In mid-December, after Begelman made restitution and agreed to get psychiatric care for the "emotional problems" that the company claimed caused these acts, Columbia announced his reinstatement.

Hirschfield and Columbia Chairman Leo Jaffe had argued unsuccessfully that Begelman should leave the company and become an independent producer. But they lost in an openly bitter dispute with two dominant board members, Herbert A. Allen, president of Allen & Co., and Matthew B. Rosenhaus, vice chairman of Nabisco, who together own 15 percent of Columbia's shares.

When Robertson read on Dec. 20 about Begelman's reinstatement, he called The Washington Post, which published the story after investigating here in New York.

Even though Begelman has quit, the Los Angeles district attorney's office said yesterday that it will continue its criminal investigation of the affair.

Columbia will not file a complaint against Begelman. Robertson, who was interviewed by the DA's office last week, said he also will not file a formal complaint but would testify if the executive is brought to trial.

A source close to Columbia said that last Friday Begelman called Hirschield in New York to request a meeting on Saturday. According to this source, Begelman told Hirschfield that "he couldn't take it anymore." He complained, said this source, that his friends, and other members of the industry were being dragged into the affair by the press.

Indeed, the Begelan affair has become a catalyst for long suppressed complaints against Columbia and other studios by actors, directors and independent producers. The most often repeated complaint is that, through complex contractual arrangments, the studios have cheated them of a full participation in the profits from movies in which they were involved.

Sean Connery recently sued Allied Artists Picture Corp. for allegedly withholding a share of the profits he said were owed to him for his role in "The Man Who Would Be King." Yesterday, Allied sued Connery for $21.5 million for defamation, malicious interference and prima facie tort.

In yet another legal wrangle growing out of the affair, Begelman has threatened to sue the sister publications New York and New West magazines over a story citing allegations that he misappointed $100,000 from the late Judy Garland while he was her manager. The allegations were included in a 12-year-old lawsuit brought by Sid Luft, a former husband of the entertainer.