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Revista EIA

Print version ISSN 1794-1237

Abstract

POVEDA RAMOS, Gabriel. AN ELECTRICAL MODEL OF ALGEBRAIC STRUCTURES. Rev.EIA.Esc.Ing.Antioq [online]. 2013, n.20, pp.183-191. ISSN 1794-1237.

Textbooks and courses in Abstract Algebra (or Modern Algebra) present and explain several kinds of algebraic structures -such as abelian groups, vector spaces, rings, ideals and fields- as if these were "free constructions of the human spirit". Usually mathematicians treat these structures as defined and analyzed in terms of operations which are characterized by properties which are presented as if comming up from a theoretical and purely platonic vacuum of ideas, in spite that they have been obtained indeed by inference and abstraction from well know, concrete operations in subjects such as Euclidean Geometry, Number Theory and Real Analysis. No considerations are done in those books about the existence and knowledge of physical objects endowed with mutual linkages, which are faithful models (or examples) of such algebraic structures with their inner operations. This paper presents one of those models, consisting of a class of electrical objects, the so-called electrical quadrupoles, which may be mutually connected in parallel (representing an "addition" between them) or in series (representing a "product" between them). Analysing these systems and these electrical operations, it is shown here how to construct a model of several of the above mentioned algebraic structures.

Keywords : Abstract Algebra; Electric Circuits; Physical Models; Groups (in Algebra); Rings (in Algebra); Fields (in Algebra).

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