From Diablo Wiki
Amethysts are one of the four types of gems found in Diablo III.
During the first year of Diablo 3, Amethysts showed the most divergence in value between softcore and hardcore. They became the least valuable gem for Softcore characters, since adding Vitality, Life, or Life on Hit is not a real priority for immortal characters.
In Hardcore on the other hand, Amethysts became the most popular and valuable gem, since mortal characters need all the health they can get.
 Amethyst Stats
 Diablo II Amethyst
Though, their stats are not the same as Amethysts in Diablo III.
Amethysts in Diablo II: Lord of Destruction:
|Quality||Weapon||Helm or Armor||Shield||Clvl Req|
|Chipped||+40 to Attack Rating||+3 to Strength||+8 to Defense||1|
|Flawed||+60 to Attack Rating||+4 to Strength||+12 to Defense||5|
|Normal||+80 to Attack Rating||+6 to Strength||+18 to Defense||12|
|Flawless||+100 to Attack Rating||+8 to Strength||+24 to Defense||15|
|Perfect||+150 to Attack Rating||+10 to Strength||+30 to Defense||18|
|Items of Diablo III  Item Basics Normal Items Legendary Armor I Legendary Armor II Legendary Weapons 1h Legendary Weapons 2h Item Sets|
|Item Basics||Item Modifiers||Inventory||Artisans||Merchants||Miscellaneous |
|Armor - Class-Specific||Weapons - Class-Specific||Crafting Items||Other Items |
|| • Blacksmith Plans
|Waist||Wrists & Hands||Legs & Feet||Head |
|| Voodoo Masks - WD|
| Chest Armor
|| Amulets cont.
|| Rings cont.
40) Puzzle Ring
|| Sources - Wiz|
|| Fist Weapons - Monk
|| Mighty Weapons - Barb|
|| Daibos - Monk
|| Bows |
|Item Sets |