1706, "a hollow," especially "the socket of a tooth," from Latin alveolus "a tray, trough, basin; bed of a small river; small hollow or cavity," diminutive of alvus "belly, stomach, paunch, bowels; hold of a ship," from PIE root *aulo- "hole, cavity" (source also of Greek aulos "flute, tube, pipe;" Serbo-Croatian, Polish, Russian ulica "street," originally "narrow opening;" Old Church Slavonic uliji, Lithuanian aulys "beehive" (hollow trunk), Armenian yli "pregnant"). The word was extended in 19c. anatomy to other small pits, sockets, or cells.
word-formation element meaning "pertaining to, of the nature of," from Latin -arem, -aris "of the kind of, belonging to," a secondary form (by dissimilation) of -alis, used after syllables with an -l- (such as insularis for *insulalis, stellaris for *stellalis).
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Definitions of alveolar from WordNet
pertaining to the tiny air sacs of the lungs;
pertaining to the sockets of the teeth or that part of the upper jaw;
a consonant articulated with the tip of the tongue near the gum ridge;