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出版Mathematics Research Center, United States Army, University of Wisconsin
URLhttp://books.google.com.hk/books?id=5lRKNwAACAAJ&hl=&source=gbs_api
註釋In this report the concept of graduated logarithmic field is defined and developed. A graduated logarithmic field is a graduated field, (introduced by the author: On the algebraic closure of certain partially ordered fields, Trans. Amer. Math. Soc. 105 (1962) pp. 229-250), which is endowed with a differentiation operator D and with logarithms i.e. solutions of the equations Dxi sub O = 1, xi sub O Dxi sub 1 = 1, xi sub O xi sub 1 Dxi sub 2 = 1 ... ; the operator D is postulated to have a certain stability with respect to the partial order in the underlying graduated field. In this abstract setting, the algorithms of the principal monomial, and of approximate factorization (introduced by the author in a functiontheoretic setting (Mem. Amer. Math. Soc. Nos. 13 and 26) are carried out in a greatly generalized form and given new interpretations in terms of the concept of stability. (Author).