THE GREAT battle over Alaska'a future has finally ended.The House of Representatives meekly accepted last Wednesday the bill the Senate passed last summer and sent it along to President Carter for his signature. The bill is a notable, perhaps stupendous, step forward in preserving a part of the original America for future generations to enjoy and use.But it is also a disappointment. It could have been -- should have been -- better.

The decision not to try to improve that Senate bill during this lame duck session, however, was inevitable once the election results were in. While the votes seemed to exist in both houses of Congress for a better bill, any effort to capitalize on them risked losing the whole project to a Senate filibuster. A failure to enact any legislation this year would have left the future of Alaska to those not all that sympathetic to preservation and conservation.

This probably rankles with the prople who fought so long to keep a larger part of the state free from mining, logging and development. But the bill now on the president's desk is still the most important piece of conservation legislation in decades. It sets aside in various categories of federally protected land an area larger in size than the state of California. It is a more sweeping bill than almost any conservationist expected to get when the Alaska issue finally gained congressional attention in the mid-1970s.

Next year the efforts will begin to change some of the bill's most controversial provisions. Alaska's representatives in Congress have already said they will attempt to "unlock" more of that state's mineral resources. The Alaska Coalition, an umbrella organization of conservation groups, has said it will be back with amendments to undo some of the more glaring errors in the Senate bill.

For the moment, however, there is enough in the bill the president will almost certainly sign to permit each side to cheer loudly. The Alaskan state government and its friends on Captiol Hill have won immediate access to much land for development. The conservationists have won the protection they sought for the heart of Alaska's natural beauty and have steered through Contress a bill that ranks in importance with the founding of the national park system a century ago.