Accession Number : AD0600738

Title :   SYMMETRY AND ESSENTIAL SYMMETRY IN GRADUATED FIELDS.

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Strodt,Walter

Report Date : MAR 1964

Pagination or Media Count : 1

Abstract : In the asymptotic theory of non-linear differential equations it is frequently important to have a precise asymptotic description not only of the elements of the coefficient field, but also of the real parts of these elements. To secure such a description the present paper introduces into the theory of graduated fields a concept of Schwarzian symmetry, and a certain concept of topological closure, and, depending upon both of these, a concept of essential symmetry. The central result presented is the following theorem: If F sub 0 is essentially symmetric, so is the algebraic closure of F sub 0. This is proved in an abstract setting which uses and develops the author's theory of graduated fields, as introduced in On the algebraic closure of certain partially ordered fields. Trans. Amer. Math. Soc. vol. 105 (1962) pp. 229-250.

Descriptors :   *ALGEBRAIC TOPOLOGY, *SET THEORY, *FUNCTIONS(MATHEMATICS), NUMBERS, ALGEBRA, TOPOLOGY, NONLINEAR DIFFERENTIAL EQUATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE