Ordered Algebraic Structures: Proceedings of the Caribbean Mathematics Foundation Conference on Ordered Algebraic Structures, Curaçao, August 1988

ISBN-13: 9789401076159 / Angielski / Miękka / 2011 / 282 str.

Jorge Martinez

Opis

'Et moi, ...si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alit.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bcll o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nOD- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Spis treści

One: Groups.- Lattice-Ordered Groups of Divisibility: An Expository Introduction..- Universal Aspects of the Theory of Lattice-Ordered Groups..- Recent Results on the Free Lattice-Ordered Group over a Right-Order able Group..- Non-Amalgamation and Conjugation for ?-Metabelian Lattice-Ordered Groups..- Periodic Extensions of Ordered Groups..- The Gate Completion G: of a Lattice-Ordered Permutation Group..- Telling Left from Right..- Applications of Spaces with Filters to Archimedean ?-Groups with Weak Unit..- Prime Ideal and Sikorski Extension Theorems for some ?-Groups..- Some Applications of Definable Spine Analysis in Ordered Abelian Groups..- Two: Rings.- Ordered Algebraic Structures in Analysis..- Rings of Continuous Functions from an Algebraic Point of View..- On Some Classes of Lattice-Ordered Algebras..- Primary ?-ideals in a class of f-rings..- Epimorphisms of f-rings..- Representation of a Real Polynomial f(X) as a Sum of 2m-th Powers of Rational Functions..- Partially Ordered *-Division Rings..- Lattice-Ordered Division Rings Exist..- Vector-Lattices and a Problem in Geometry..- Banaschewski Functions and Ring-Embeddings..- On Orderpotent Rings..- A Sampling of Open Problems.