Oystein Ore: Algebraic Structures

Leo Corry
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Leo Corry: Tel Aviv University, The Cohn Institute for the History and Philosophy of Science and Ideas

Chapter Chapter 6 in Modern Algebra and the Rise of Mathematical Structures, 2004, pp 259-288 from Springer

Abstract: The first reflexive attempt to develop a formal theory of structures that we consider here is the research program initiated by the Norwegian mathematician Oystein Ore, beginning in 1935 at Yale. Ore’s program was an attempt to develop a general foundation for all of abstract algebra based on the concept of lattice, which he denoted with the term structure. The leading idea behind this attempt was that the key for understanding the essential properties of any given algebraic system lay in overlooking not only the specific nature, but even the very existence of any elements in it, and in focusing on the properties of the lattice of certain of its distinguished subsystems. Ore intended to derive, in this way, all the main, general theorems valid for all algebraic domains.

Keywords: Boolean Algebra; Algebraic Structure; Lattice Theory; Decomposition Theorem; Universal Algebra (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-0348-7917-0_7

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