SUT J. Math. 32 (1), 59-66, (January 1996) DOI: 10.55937/sut/1262208499
Takeo Ohi, Hirokazu Nagai
KEYWORDS: differential module, residue map, residue free, differential of second kind, 13N05, 12H05
Let be a field of characteristic 0, an -dimensional non-singular algebraic variety over the function field of and the module of differentials of over . A closed differential is called residue free if for any prime divisor of and a differential is called second kind if for any prime divisor , there exists an element such that , where is the canonical valuation with respect to . In this paper, we prove the following theorem: Let be a closed element of . Then is residue free if and only if is of second kind.