Acting in a case of purported sex discrimination against men, the Supreme Court agreed yesterday to decide whether Missouri can deny widowers the same workmen's compensation death benefits that it pays widows.

The justices agreed to review a 5-to-1 ruling in which the state Supreme Court upheld a law allowing a widower who is not mentally or physically incapacitated to collect death benefits only if he proves he had been dependent on his wife's wages for support.

By contrast, the law presumes that a widow had been totally dependent upon her husband's support and automatically awards her death benefits.

The Missouri tribunal, rejecting a claim that the law denies the equal protection of the laws guaranteed by the Constitution, upheld the refusal of $30,000 to $40,000 in death benefits to Paul Wengler, a financially independent liquor store owner whose working wife died in a job-related accident. Had he been killed, she would have collected routinely.

In most states, workmen's compensation laws ignore the sex of a surviving spouse. The Missouri law was enacted in 1925, when states generally assumed that widows faced more urgent economic problems than widowers

The court took these other actions: VIETNAM VETERANS

In 1969, Thomas E. Coffy left his job as a Republic Steel Corp. crane operator for two years' miltary service. The job was his when he returned -- but he was laid off before he could resume it. With that, he found he had another problem: by serving in the armed forces, he had lost roughly half of the supplemental unemployment benefits he would have had if he had stayed on the job.

In his behalf, the government argued that a 1974 law, the Vietnam Era Veterans Readjustment Assistance Act, guaranteed, as a "perquisite of seniority," the benefits of which he had been deprived.

The 6th U.S. Cricuit Court of Appeals agreed with Republic Steel that "services rendered," not seniority, determined the amount of benefits to be awareded, and that Coffy's military stint consequently did not count. But that ruling conflicted with decisions in similar cases by the 3rd and 7th circuits.

Yesterday, the Supreme Court agreed to try to resolve the conflict. SMOKING ON THE JOB

The court left standing a ruling that the Occupational Safety and Health Act does not empower federal employes to sue bosses for allowing smoking at worksites. INIDIGENT MOTHERS, CHILDREN

In Van Wert, Ohio, last year, a juvenile court ruled that Pamela O. Suebler, an indigent, had neglected her children, Angela, 3, and Terry, 6 months, and assigned permanent custody to the county welfare department.

To fight the fuling, Subler needed, but had no money for, a transcript of the juvenile proceeding. Her request to a state appeals court to pay for the transcript was refused on the ground that the tribunal was not authorized to do that. The Ohio Supreme Court dismissed her appeal of the refusal.

The appellate court then held that it had to throw out the case because she had not supplied the transcript. Returning to the state's highest court, Subler claimed that the state was taking her children in violation of the constitutional guarantees of due process and equal protection of the laws.

In May, the state high court held the case raised no substantial constitutional question. Yesterday, however, the U.S. Supreme Court granted Subler's petition for review. "THE ARNHEITER AFFAIR

The court turned down appeals by purported defamation victim Marcus A. Arnheiter, a former Navy officer who had sued author Neil Shechan, the hardcover and paperback publishers of his 1972 book, "The Arnheiter Affair," the National Broadcasting Co., and Johnny Carson, who had interviewed Sheehan on NBC's "The Tonight Show."

Cmdr. Arnheiter commanded the USS Vance, a warship assigned to patrol duty off the coast of Vietnam, but was relieved by the Navy after 99 days. The book was an account of Arnheiter's command. RUSSELL LITTLE RETRIAL

The court let stand a lower court ruling granting a new trial to Symbionese Liberation Army member Russell J. Little, who was convicted four years ago of the ambush murder of Oakland, Calif., school superintendent Marcus Foster.

A California Court of Appeal threw out Little's murder conviction because of improper jury instruction.

The action by the high court removed the last chance California and Alameda County, Calif., prosecutors had of overturning the appeals court ruling, they said they now expect Little to be retried early next year.

Little, who also has been convicted of an attempted escape, is imprisoned in Vacaville, Calif.

Foster was shot with cyanide-tipped bullets as he walked to his car after a meeting of the oakland school board. The SLA later claimed responsibility for Foster's death.