SAN FRANCISCO (Reuters) - Police in the San Francisco Bay Area were searching on Monday for a 57-year-old woman who was kidnapped for ransom, officials said, even though her suspected abductors have been arrested.

Police in the city of Vallejo said Elvira Babb was reported kidnapped on July 1 by her son, who had received a text message the night before from an unknown number saying his mother had been taken, demanding money, and saying she would be killed if he contacted police.

Last week, police arrested four people in relation to the kidnapping: Emmanuel Espinoza, 26; Jalon Brown, 32; Larry

Young, 23; and Lovely Rauzol, 27.

Espinoza and Young were arraigned on Monday, Vallejo Police Lieutenant Jeff Bassett said. Local broadcaster KRON4 said Espinoza pleaded not guilty while Young is attempting to hire an attorney and did not enter a plea.

Bassett said Rauzol and Brown were both set to be arraigned on Tuesday.

Police said the suspects have been uncooperative with authorities in their search for Babb. The search has been aided by other local law enforcement agencies, the U.S. Marshals Service and the Federal Bureau of Investigation.

The abduction comes after the Vallejo Police Department was sued in March by a couple who said their reputations were destroyed after one of them reported that the other had been kidnapped and police described the incident as a hoax.

(Reporting by Curtis Skinner in San Francisco; Editing by Andrew Hay)