Abstract
This chapter deals with basic notions (divisibility, units, irreducible elements, Euclidean rings, and principal ideal domains) in general domains.
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Notes
- 1.
The standard example of a domain without 1 is the ring of even integers.
- 2.
Étienne Bézout (1730–1783) was a French mathematician, an author of textbooks. Bézout proved the existence of Bézout elements for polynomial rings; in the case of integers, they already occurred in the work of Bachet .
References
P.G.L. Dirichlet, Vorlesungen über Zahlentheorie, 2nd edn., ed. by R. Dedekind (Brunswick 1871); English translation Lectures on Number Theory (American Mathematical Society and London Mathematical Society, London , 1999)
K. Plofker, Mathematics in India (Princeton University Press, Princeton, 2009)
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Lemmermeyer, F. (2021). Divisibility in Integral Domains. In: Quadratic Number Fields. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-78652-6_4
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DOI: https://doi.org/10.1007/978-3-030-78652-6_4
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