1) Chain armor 2) Chain armour 3) Chain mail 4) Mail 5) Ring armor 6) Ring armour 7) Ring mail 
sleeveless mail coat
• (n.) Properly, a short hauberk, but often used loosely for the hauberk.
Ha·ber'ge·on (hȧ*bẽr'je*ŏn or hăb'ẽr*jŭn) noun [ French haubergeon a small hauberk, dim. of Old French hauberc , French haubert . See Hauberk .] Properly, a short hauberk, but often used loosely for the hauberk. Chaucer. 
Habergeon was a sleeveless jacket of chain-mail, shorter than the hauberk, and worn by squires and archers during the Middle Ages.
[n] - (medieval) a light sleeveless coat of chain mail worn under the hauberk
noun (Middle Ages) a light sleeveless coat of chain mail worn under the hauberk