Jade was the daughter of the original Green Lantern, Allan Scott. Although some of Jade's powers did come from her father, she did join the Green Lantern Corp, while dating the current Green Lantern, Kyle Rayner. To help in his endeavours to fight evil, he created a ring from his own (not a specifically different ring, as each Green Lantern has) but more of an extension of his own.

There are many many more female Green Lantern that populate the Green Lantern Corp. Green Lanterns come from all galaxies, planets, races and genders. Most people are just more familiar with the Green Lanterns that are protecting Earth's sector.

Allan Scott
Hal Jordan
Guy Gardner
John Stewart
Kyle Rayner

Although recently Kyle's power have transformed to a level that has made him into Ion, while Hal Jordan has returned from the Pharallax entity and is again the Green Lantern of Earth's sector.