Fields, Rings, and Ideals

J. J. P. Veerman ()
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J. J. P. Veerman: Portland State University

Chapter Chapter 7 in Numbers from all Angles, 2026, pp 123-146 from Springer

Abstract: Abstract The characteristics of $$\mathbb {Z}$$ Z are so familiar to us, that it is hard to break through that familiarity to understand what makes things like unique factorization tick. Algebraic number theory Algebraic number theory and with it large swaths of algebra were developed to deal with more general number systems in order to overcome this problem. So in this chapter, we initially move away from the usual integers a little to study concepts of abstract algebra. This discipline of mathematics seems to start with a daunting barrage of definitions or nomenclature. Here, we look at some of these and relate them as much as possible to their origins in number theory.

Date: 2026
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DOI: 10.1007/978-3-032-10000-9_7

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