ariyāyetaṁ

Contracted sandhi form for ariya + āya + etaṁ; nominative singular neuter of ariya (noble) + dative singular of ariya + nominative singular neuter of etaṁ (this)

for the noble one (this)
in the noble way (this)

Built from

ariya — root · noble, worthy
Adjective from PIE *ar- (fit, suitable). In canon, ariya denotes those following the Buddha's path and the qualities of moral excellence and inner refinement.
āya — ending · dative
Dative singular ending; marks recipient or beneficiary (to, for). Historically from PIE *-ai.
etaṁ — root · this
Demonstrative pronoun, nominative neuter singular; from PIE *e-t- (this one), cognate with Latin is/id and English that.

Analysis. ariya (noble, worthy) + āya (dative ending; to, for) + etaṁ (this, neuter) — contracted through vowel elision and palatalization at word boundary. The form appears where 'this is for the noble one' or 'this pertains to the noble path' is meant.

Etymology. ariya derives from PIE *ar- (fit, suitable); cognate with Sanskrit ārya (noble, of the Aryans) and Greek arete (excellence, virtue). The dative suffix -āya is from PIE *-ai (to, for), cognate with Latin -ae (dative) and English goal-marking 'to'.

Meanings from the Digital Pāḷi Dictionary; morphology and etymology by Claude.

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