A UNIVERSITY, according to the standard definition, is an educational institution of the highest order with one or more undergraduate colleges, a program of graduate studies and a number of professional schools. But that leaves out one critical part of a modern university's function: football--what else?

Reflect on the battle now under way between the National Collegiate Athletic Association and the College Football Association. It is, as best we can make out, over money and a television contract worth millions of dollars a year. A majority of the 61 "major football schools," as the members of the CFA are widely known, wants to control its own rules and its own TV contracts. The NCAA, to which these as well as hundreds of other schools belong, wants to keep on controlling those rules and contracts as it has in the past.

Whatever the merits of the issues in dispute--such matters as academic eligibility standards and who "owns" the television rights to each football game-- they are overshadowed by money. The NCAA signed a contract last July to let ABC and CBS televise selected college games between 1982 and 1985 for $263.5 million. The CFA has tentatively approved a contract with NBC to let it televise games during those same years for $180 million. Many of the games are the same, and the question is not only who gets to televise what but, equally, who gets to share in the pot of gold. Because their games are the bigger attractions, the "major football schools" want a bigger cut than the NCAA proposes to give them.

Regardless of who wins, the dispute will help bring the relationship between universities and football into a clearer perspective. Football teams that play in the big-time leagues are not an extension of academic life onto the playing fields but rather an exercise in making money. At those schools, this sport--and, in some places, basketball as well--is a business in which the bottom line of the financial ledger is far more important than school spirit, sportsmanship and amateurism. Some years ago, we suggested--not entirely in jest--that those schools give up the facade of intercollegiate athletics and declare themselves to be the owners of minor league franchises.

Maybe the confrontation between the CFA and the NCAA is a step in that direction. If not, something else will be. After all, how long are so many intelligent young men--they must be intelligent because they are university students--going to play for peanuts when the schools they play for are making millions?