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Please use this identifier to cite or link to this item: http://hdl.handle.net/11133/354

Title: 形式的ベキ級数環における高階微分について
Other Titles: On Higher Differentials in Formal Power Series Rings
Authors: 荒木, 淳
ARAKI, Atsushi
Issue Date: 30-Mar-1974
Publisher: 愛知工業大学
Abstract: In [1], the concept of higher differentials in a commutative ring (by means of universal higher derivation) was introduced and it was shown that if a geometric regular local ring R is regular, then the submodule A^n(R) of A(R) generated by elements of degree n over R is R-free. In this paper, we shall consider the case where R is a formal power series ring. When R is a residue class ring k[[X_1,…, X_S]]_q/pk[[X_1,…, X_s]]_q where p, q are prime ideals in k[[X_1,…, Xs]] such that p⊂q, we have the following result under some conditions: The submodule A^n(R) of A(R) generated by elements of degree n over R is R-free if R is regular.
URI: http://hdl.handle.net/11133/354
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