The politicians in Ohio are having a hard time keeping their eyes focused on Tuesday's presidential primary. The November general election in this state looks a lot more interesting, and probably as pivotal as any in the country.

President Carter came to Columbus and Cleveland Thursday for his first acknowledged political trip of the year, telling receptive crowds that he expected Ohio -- which gave him the votes that cinched his nomination in 1976 -- "will make a decision that will give me a nationwide majority of the Democratic delegates again."

That forecast is supposed by every public and private poll. Even Paul Tully, Ohio campaign manager for Sen. Edward Kennedy (D-Mass.), concedes that Kennedy probably trailed the president by 15 points going into the final days -- and is being outspent by a 6-to-1 ration ($400,000 to $65,000) on radio television.

Kennedy, who is generally given a better chance of upsetting Carter in News Jersey and California, the other two big states that vote Tuesday, was in Ohio three times this week.

But he was upstaged by the preview of the fall campaign between Carter and prospective Republican candidate Ronal Reagan, who moved across the state for three days and almost crossed paths with Carter in Columbus.

The Reagan tour was scheduled before George Bush's withdrawal sewed up the GOP nomination for the former California governor. But Reagan kept to his orignial schedule as a down payment for the Autumn fight to bring back the Republican Column the 25 Ohio electoral votes that Gerald R. Ford lost to Carter by only 11,116 votes, of more than 4 million that were cast.

The focus on the coming Carter-Reagan contest kept Kennedy from getting much press with his contiuing debate challenges or his condemnation of Carter economic policies before responsive crowds of unemployed steel and auto workers.

The sharp decline in Ohio's steel, tire and auto industries has given Kennedy an opening. Unions like the United Auto Workers are urging their members to vote for Kennedy "as a way to "send Washington a message that the workers of Ohio will not continue to carry the burden of an ecomomy gone out of control."

But the "send them a message" theme is also an implicit acknowledgement that Kennedy has problems with blue-collar voters -- as he has had almost everywhere west of the Alleghenies -- because of the character questions. The Carter campaign has been running the same anti-Kennedy spots it used to stalemate him in Pennsylvania -- and Tully concedes that "it's harder with urban Catholics and ethnics here than it was in Philadelphia. But it's nowwhere near as tough as it was in Chicago," where Kennedy was wiped out.

The prospect of a light primary vote may work to Kennedy's advantage, his backers say they think, but Carter has a strong base in southern and central Ohio -- culturally more like the South than the Northeast.

Carter also has an "in" with the liberal community through Dick Celeste, the former lieutenant governor, who took time off from his duties as director of the Peace Corps to campaign this week for Carter.

The Carter-Kennedy fight has split the state Democratic establishment. Carter has the support of Sen. John Glenn (D-Ohio), but Sen. Howard M. Metzenbaum (D-Ohio) is backing kennedy, as is Cuyahoga Country (Cleveland) Democratic chairman Tim Hagen, one of the original draft-Kennedy leaders, now busy with his own race for county commissioner.

The black leadership is similarly divided. Carter is backed by C. J. McClin Jr., the Dayton legislator who is the strongest black leader outside Cleveland. Kennedy has Rep. Louis Stokes, the leader of Cleveland's predominantly black 21st District, but Carter was able to enlist the help of George Forbes, the black president of the Cleveland City Council.

Despite his long absence from the campaign trail, Carter showed the kind of fast footwork it takes to survive in such a polarized political community.

At 6 p.m., he was standing in Parma, a white ethnic enclave, with a mayor whose administration is the target of a Justice Department suit for exclusionary segregated practices.

And at 7:30 p.m. he was telling the audience in a black church across town that he was proud that a black man, Drew Days, is now the assistant attorney general enforcing the civil rights laws.

The Celeste organization, assembled for a losing 1978 guernatorial bid and in readiness for another try in 1982, is the heart of the Carter campaign. aCeleste said he thought until two weeks ago that Carter would do well to beat Kennedy by six points. But he said the withdrawal of Bush from the GOP primary "has made this more of a general-election situation," with Kennedy's candidacy no longer seeming relevant.

Now, he says, Carter has a chance to gain a standoff with Kennedy in the northern Ohio industrial belt.

But, for the fall, it is another story. Carter forces are working hard to keep Independent John B. Anderson off the Ohio ballot -- a symptom of their nervousness.

But a lawyer familiar with the case says Anderson has at least a 50-50 chance of winning his federal court challenge to the March 20 Ohio filing deadline, in a case that seems certain to wind up in the U.S. Supreme Court.

Paul Tipps, the state Democratic chairman and a Carter backer, says that with Anderson on the ballot, Carter's chances of carrying Ohio "depend heavily on how well we do with the Kennedy people . . . It will be a tough to carry Ohio without a united Democratic effort."

"All they [the Carter people] want to do is destroy him, to keep him and all other Kennedy's from running in the future," says former state Democratic Party chairman Pete O'Grady. "It's good politics, sure, but what kind of platform does that leave Carter to run on in November?"

But if the Democrats are worried, so are the Republicans. Reagan's tour, led and promoted by Ohio Gov. James A. Rhodes, drew meager crowds for the main public rallies in Cincinnati, Columbus and Cleveland -- with fewer than 10,000 people seeking him in the three cities' central square rallies timed for lunch breaks or evening office-closings.

Earl Barnes, the state GOP chairman, and Bob Hughes, the Cuyahoga County chairman, both think Reagan can win, because, as Barnes put it, "this state is oriented to jobs, and Carter's record is looking really bad."

But Barnes and Hughes also said that Reagan needs help from a more moderate GOP runningmate. "Maybe because of his age, or for other reasons," Barnes said, "there's an inordinate amount of interest in who his vice president will be."