Algebra

Lars Gårding
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Lars Gårding: Mat. Inst.

Chapter 3 in Encounter with Mathematics, 1977, pp 23-56 from Springer

Abstract: Abstract The word algebra is part of the title of an Arabic manuscript from about 800 A.D. giving rules for solving equations, and until about 100 years ago algebra was just the theory of equations. Nowadays it is best described as dealing with more or less formal mathematical operations and relations. Modern algebra is really a collection of second generation abstract models drawn from many parts of mathematics. Economy of notation prescribes that new symbols should be avoided unless absolutely necessary. For this reason familiar operational signs, e.g., those for addition and multiplication, are used again and again but acquire new meanings depending on the model. The objects of algebra are classified by the kind of operations that can be performed in them. They carry names like “ring” and “ideal,” which may sound funny at first; but this feeling wears off with a closer acquaintance.

Keywords: Maximal Ideal; Commutative Ring; Galois Group; Permutation Group; Division Ring (search for similar items in EconPapers)
Date: 1977
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DOI: 10.1007/978-1-4615-9641-7_3

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