A Jew must not walk around with his head non-covered (Shu"A Orach Chayim 2,6 " ולא ילך ארבע אמות בגילוי הראש מפני כבוד השכינה).
Is a gentile required to cover his head while studying Torah? If a gentile studies Torah without his head covered, is he violating a rabbinical commandment?