Is it obligatory for a man to cover his shoulders during prayer, and is his prayer valid if his shoulders are uncovered?

The jurists agreed on the obligation of covering the 'awrah (private parts) during prayer, but they differed on the obligation of covering the 'atiq (the area between the shoulder and the neck). The majority of scholars held that it is not obligatory, while the Hanbalis held that it is obligatory, especially in obligatory prayers, citing the hadith: "None of you should pray in a single garment with nothing on his shoulders."

As for the majority, they cited Jabir's hadith: "If it is wide, wrap yourself in it; and if it is narrow, use it as an izar (waist wrapper)." They interpreted the prohibition in Abu Hurayrah's hadith as a recommendation, and they believe that covering the shoulders is not because they are 'awrah, but for the completeness of the dress and to secure the izar.

In summary: It is not obligatory for a man to cover his shoulders or 'atiq during prayer, but it is recommended for adornment and to venerate the prayer. If he prays with uncovered shoulders or 'atiq, his prayer is valid.