Other known names: Ajax, Aias (Of the Earth)
Son of Telamon, king of Salamis, a legendary hero of ancient Greece. To distinguish him from Ajax, son of Oileus, he was called "Ajax the Great" or "Telamonian Ajax"

Traits and Characteristics:
He is an individual of great stature and colossal frame. Considered only second to Achilles in terms of strength and bravery. He was trained by the centaur Chironexternal image ExekiasAjax.jpg (who had also trained his father, Heracles, and Achilles' father Peleus), at the same time as Achilles was. Ajax was the most valuable king in the battlefield, though not as smart as Nestor, Idomeneus, or, of course, Odysseus. He commanded his army wielding a great axe and a huge shield made of seven ox-hides with a layer of bronze, always accompanied by the prince Teucer. He was indeed a great asset to king Agamemnon's army. He is not wounded in any of the battles described in the Iliad, and he is the only principal character on either side who does not receive personal assistance from any of the gods who take part in the battles. As such, he embodies the virtues of hard work and perseverance.

In the Trojan War:
During the Iliad, Ajax is notable for his two fights with Hector. The first time is in a duel which lasts most of a whole day. Ajax and Hector both fail to wound each other mortally and ended with a draw, resulting in their exchanging of gifts.
The second fight occurs when Hector breaks into the Achaean camp, and fights with the Greeks among the ships. Ajax throws a giant rock at Hector which almost kills him. Later, Hector regains his strength and makes an assault that almost finishes the war. As this was happening, Ajax was able to kill a lot of Trojan leaders.
Later, when Achilles dies, killed by Paris, Ajax and Odysseus are the heroes that fight against the Trojans to get the body and bury it next to his lover, Patroklos. After Ajax and Odysseus burry Achilles body, Odysseus gets Achilles' armor as credit. Ajax is furious about it, and falls to the ground, exhaustedexternal image DeathOfAjax.jpg. When he wakes up, he becomes mad and goes to a group of sheep, and slaughters them, imagining they're the Trojan leaders, as well as Odysseus and Agamemnon. When he comes to his senses, covered in blood, and realises what he did, he decides that he prefers to kill himself rather than to live in shame. He did it with the same sword Hector had given him when they exchanged presents.
Effects on the Community:
Ajax is the tutelary hero of the island of Salamis, where he had a temple and an image, and where a festival called Aianteia was celebrated in his honor. At this festival a couch was set up, on which the panoply of the hero was placed, a practice which recalls the Roman lectisternium. He was worshipped at Athens, where he had a statue in the market-place, and the tribe Aiantis was called after his name.


AJAX-a brand of soap/detergent
Sources:
http://www.biographybase.com/biography/Ajax_the_great.html
http://www.answers.com/topic/ajax
http://www.mlahanas.de/Greeks/Mythology/Ajax.html
http://images.artwanted.com/large/95/6679_33295.jpg
http://www.mlahanas.de/Greeks/Bios/ExekiasAjax.jpg