Dedekind domain：Introduction
Introduction
Dedekind Domains
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Definition 1 A Dedekind domain is an integral domain that has the following three properties: (i) Noetherian, (ii) Integrally closed, (iii) All non-zero prime ideals are maximal.
Dedekind domain
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In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors ...
m3p8 lecture notes 11
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The reason Dedekind domains are interesting to us is that the nonzero ideals in a Dedekind domain factor uniquely as products of prime ideals. The idea to study ...
NOTES ON DEDEKIND RINGS Contents 1. Fractional ...
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An integral domain R is a Dedekind ring (or Dedekind domain) if every non-zero ideal of R is invertible. A discrete valuation ring, or DVR, is a local.
3 Properties of Dedekind domains
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In the previous lecture we defined a Dedekind domain as a noetherian domain A that satisfies either of the following equivalent conditions:.
Dedekind Ring
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The main example of a Dedekind domain is the ring of algebraic integers in a number field, an extension field of the rational numbers. An important consequence ...
abstract algebra
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Let A be a Dedekind domain. PID implies UFD. So for the other direction assume A is an UFD. In this proof the author only considers prime ideals ...