One of the three Elvish rings of power, the Ring of Air (S/288). It might simply be vilya “air” used as a name. However, given the pattern of names for the other Elvish rings, I think it is more likely to be an adjectival formation combining the root ᴹ√WIL and the adjectival suffix -ya.
Quenya
vilya
noun. air, sky
vilya
proper name. (Ring) of Air
vilya
air, sky
vilya noun "air, sky", also name of tengwa #24. Older wilya. (Appendix E). Early "Qenya" has Vilya (changed from Vilna) "lower air" (LT1:273); also vilya "air" (MC:215)
vilwa
air, lower air
[vilwa < wilwa] noun "air, lower air" (distinct from the 'upper' air of the stars, or the 'outer') (WIL; in one place vilwa was not struck out, VT46:21) According to VT46:21, Tolkien considered vilda < wilda as a replacement form, but rejected it.
wilya Archaic
noun. air, sky
lindë
air, tune, singing, song
lindë noun "air, tune, singing, song" (SA:gond, (LIN2, [GLIN]); lindelorendor "music-dream-land"; see laurelindórenan lindelorendor... _(LotR2:III ch. 4, cf. Letters:308). _Also compare lindi- in lindimaitar, q.v. (but the other compounds here cited do not give a lindë a stem-form lindi-).
wilma
air, lower air
wilma noun "air, lower air" (distinct from the 'upper' air of the stars, or the 'outer') (WIL)
A word for “air” or “sky” appearing Appendix E of The Lord of the Rings from older †wilya, serving as the name of tengwa #24 [n] (LotR/1123). It is clearly a derivative of the root ᴹ√WIL (Ety/WIL). It has an abnormal plural form wilyar with initial w- in the 1950s version of the Nieninquë poem in the phrase yan i wilyar antar miquelis “✱to whom the air gives kisses” (PE16/96).
Conceptual Development: The notion of the “lower air” as a region dates all the way back to the earliest Lost Tales, where the innermost layer of air was called ᴱQ. Vilna (LT1/65). However, in the Qenya Lexicon of the 1910s, the term was ᴱQ. Vilya “air (lower)” as a derivative of the early root ᴱ√VILI (QL/101). The word vilya “lower air” appeared English-Qenya Dictionary of the 1920s but was deleted (PE15/68), and this term appeared as both the singular “air” and plural “airs” in version of Nieninqe and its drafts circa 1930: yan/yar i __vilya(r)__ anta miqilis “to whom the air(s) give kisses” (MC/215; PE16/90, 92).
In the Ambarkanta of the early 1930s, the lower air was {Wilwa >>} Vista (SM/236, 240 note #1), but it was Wilwa again in the earliest tales of Númenor from the 1930s (LR/12) and was ᴹQ. {vilwa >>} wilma in The Etymologies of the 1930s under the root ᴹ√WIL “fly, float in air” (Ety/WIL). Q. vilya “air, sky” in Appendix E seems to be the last iteration in this chain.
Neo-Quenya: For purposes of Neo-Quenya, I think vilya refers mainly to air as the region above the ground, as opposed to ᴹQ. vista “air (as a substance)”. You breath vista, but birds fly through vilya, and breezes flow through vilya like ripples in a lake.