TRENTON, N.J. (AP) _ The Christian Science church does not have exclusive rights to that name because it denotes a system of religious beliefs, not just the church organization, the state Supreme Court ruled.

A divided court said Monday that the Boston-based First Church of Christ, Scientist, cannot trademark the name Christian Science because it does not have a monopoly over the religion. The ruling would allow the Independent Christian Science Church in Plainfield, which split from the main church, to keep its name.

The court ruled that Christian Science designates the religion founded by Mary Baker Eddy in 1866, not just the Boston-based ''mother church'' she founded several years later. The term is just as much in the public domain as Methodist or Episcopal, it said.

The mother church ''simply cannot appropriate, from the public domain, the common name of a religion and somehow gain an exclusive right to its use and the right to prevent others from using it,'' the court said.

Nathan Talbot, a spokesman for the Boston organization, said the church would not comment on the decision until it has a chance to review it.

The Plainfield church had been affiliated with the Boston organization since 1892. But a doctrinal schism that developed in 1977 prompted the parent organization to withdraw its recognition of the local church.

The Boston organization sued when the Plainfield church took the name Independent Christian Science Church.

In a dissenting opinion, two justices argued that the trial court was right when it ruled in favor of the parent organization, saying the public idenfities Christian Science with the Boston organization and would be confused if other churches used the name.