The board of trustees of the University of the District of Columbia voted last night to appoint Chicago educator Benjamin H. Alexander the university's next president.

Alexander's name was the only one recommended to the board by the eight-member search committee that has been working for more than a year to find a successor to resigning UDC president Lisle C. Carter.

Alexander, 60, has been president since 1974 of Chicago State University, a school about half the size of UDC. There, he introduced proficiency examinations that all students must pass before they can graduate, and abolished the school's no-fail grading system.

"Based on his record at Chicago State over the past eight years, I think he will be an excellent president of UDC ," said Marjorie Parker, chairman of the UDC board of trustees.

Alexander, who was in Springfield, Ill., last night on business, said in a telephone interview that he had not yet received official notification of the board's action. But, he said, "if the job is offered, I will accept it.

"My hopes are to work with the faculty, students, community and board to make UDC the best university in the area," he said.

Search committee members said they were seeking a new president with broad administrative experience who could also improve the university's academic standards and public image.

Faculty members at the university have expressed concerns about some of the more conservative stands that Alexander has taken. One faculty member who asked not to be named recalled that when Alexander was a member of the D.C. school board in the late 1960s, he called for the suspension of two teachers who had used in their classes an essay that included a four-letter word.

Alexander also has taken what some view to be conservative stands for a black educator. Throughout his career, he has defended Harriet Beecher Stowe's slave character, Uncle Tom, whose name has a derogatory meaning for many blacks, but which Alexander says connotes courage and strength of character.

He also has said that he does not feel black students necessarily need to attend school with white students.

On Monday, members of the UDC faculty senate steering committee circulated an open letter concerning Alexander that asserted that faculty members had not been given a chance to meet with the final candidates for the $59,000-a-year president's post. The president of the faculty senate, however, did serve on the search committee.

The university, which was formed through a merger of D.C. Teachers College, Federal City College and the Washington Technical Institute five years ago, is "just starting to develop its true character," said faculty senate official Meredith Rode, a professor of art at the university.

"Whoever the new leadership is will really chart the future course of the university . . . " she said. "This university needs a unifying force. It doesn't need anybody with a controversial public background."

Alexander was praised yesterday by colleagues in Chicago for having eased racial tensions at Chicago State while improving academic standards.

Alexander, whose professional background is in chemistry, lived for a number of years in Washington where he served as president of the D.C. Federation of Civic Associations and chairman of the D.C. Commission on the Arts and Humanities.