deḱ-
“to take, to accept”take, receive, accept
Root for receiving/accepting, yielding Latin decere (to be fitting), Greek dekhesthai, English decent.
Discussion
The PIE root *deḱ- (to take, to accept, to receive, to be fitting) produced one of the most socially significant word families in the IE vocabulary — connecting the act of receiving to the concepts of propriety, teaching, and human dignity.
Latin decēre (to be fitting, to be proper) continues the root and gave English: decent (befitting, proper), decorum (propriety of behaviour), decorate (to make fitting/beautiful), and dignity (dignitas, the quality of being worthy of acceptance — from dignus, "worthy," from *deḱ-no-). The semantic chain accept → fitting → proper → dignified → worthy encodes a social philosophy: what is received with approval is fitting, what is fitting is proper, and what is proper confers dignity.
Latin docēre (to teach — causative of *deḱ-, "to cause to accept") gave English: doctor (one who teaches — the doctoral title preceded the medical one), doctrine (that which is taught), document (something that teaches/proves), and docile (willing to accept teaching). The doctor is etymologically not a healer but a teacher — one who causes others to accept knowledge.
Greek dokein (to seem, to think, to accept — "it seems fitting") gave English: dogma (that which seems right, hence an established belief), orthodox (ortho-doxa, "straight-seeming" — holding the correct beliefs), paradox (para-doxa, "beside the seeming" — against expectation), and heterodox (other-seeming — holding different beliefs).
The root connects to *deyḱ- (to show, to point — see the judge/digit root) through the concept of presentation and acceptance: what is pointed out (*deyḱ-) is then received (*deḱ-).
Notes
Pokorny 189-191. English decent, dignity, doctor, docile, disciple.