Tafsir of As-Saffat 37:79

(Peace be upon Nuh) is a subject and predicate (mubtada' wa khabar). It is permissible to begin with an indefinite noun here because it carries the meaning of a supplication. The speech is presented as a narration, like your saying: "I recited 'A Surah which We have sent down'." According to Al-Farra' and other Kufans, it is a quoted utterance in the position of being the object of the verb "We left" (tarakna); that is, "We left this specific statement upon him."

Others have said: It is a quote following an implied verb, meaning: "We left for him among the later generations their saying, 'Peace be upon Nuh'." The intention is that We preserved for him the supplications and greetings of people, generation after generation. It is also said: This is a greeting from Him—the Almighty and Majestic—not from others. In this view, it is an object, and the object of "We left" is omitted; meaning: "We left for him a beautiful commendation and preserved it for him among those who came after him until the end of time." This is attributed to Ibn Abbas, Mujahid, Qatadah, and As-Suddi. The phrase "Peace be upon Nuh," according to Al-Khafaji, is the object of an implied verb, i.e., "And We said: Peace, etc." Abu Hayyan stated: It is an initial sentence; Allah Almighty greeted him with peace so that mankind might follow that example, and thus no one would speak of him with evil. Abdullah (ibn Mas'ud) recited it as "Salaman" (in the accusative case), as an object for the verb "We left."

As for His saying: (In the worlds)

It is connected to the prepositional phrase due to its acting on behalf of its implied verb, or it is connected to whatever the prepositional phrase is connected to. It is also permissible for it to be a state (hal) from the hidden pronoun within it. In any case, it is a continuation of the previous sentence, brought forth to indicate the complete importance given to this greeting, in that the speech implies its affirmation among the worlds—both the angels and the jinn and mankind—or that it is a state of him being in the worlds upon Nuh. This is like your saying: "Peace be upon Zayd in all places and at all times." Some have claimed it is permissible to consider it a substitute (badal) for His saying: "In the later generations," though this is likely an error, as is not hidden.