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- W2012515225 abstract "L. Introduction. In this paper we define a quasi-local ring R, or (R, M), to be a commutative ring with unity having a unique maximal ideal M such that nn=1 M ={O}. Thus a Noetherian quasi-local ring is a local ring. A higher derivation D = {Dj} 1 on a quasi-local ring R is said to be convergent if, for all a in R, :E?= 0 D,(a) is a convergent series in the M-adic topology. Do always denotes the identity mapping. If R is complete the mapping ocD: a -i= . Di(a) is an endomorphism of R which induces the identity mapping on the residue field of R (Lemma 1). With suitable restrictions on D, a,D is an automorphism and hence an inertial automorphism. A seemingly natural additional condition sufficient to insure that a,D is an automorphism is the condition" @default.
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- W2012515225 date "1968-01-01" @default.
- W2012515225 modified "2023-10-16" @default.
- W2012515225 title "Convergent higher derivations on local rings" @default.
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- W2012515225 doi "https://doi.org/10.1090/s0002-9947-1968-0223358-1" @default.
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