GRADUATED LOGARITHMIC FIELDS AND STABILITY,
Technical summary rept.
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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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