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Fractional ideal
A fractional ideal of R is an R-submodule I of K such that there exists a non-zero r ∈ R such that rI ⊆ R. The element r can be thought of as clearing out the ...
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Discrete valuation ring - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Discrete_valuation_ring
R is not a field, and every nonzero fractional ideal of R is irreducible in the sense that it cannot be written as finite intersection of fractional ideals properly ... |
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For each non-zero element k ∈ K, kR is an invertible fractional ideal that is ... is a Dedekind ring, all non-zero fractional ideals are invertible, and they can all be ...
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Mar 16, 2010 ... In this case, every nonzero fractional ideal is invertible, and consequently the nonzero fractional ideals in $A$ form a group under ideal ...
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We say that I is a fractional ideal of R if rI ⊆ R for some nonzero r ∈ R. We call r a ... The product of two nonzero fractional ideals is a nonzero fractional ideal, ...
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field K. A non-zero fractional ideal F of D is said to be divisorial if F is an inter- section of principal fractional ideals of D [4; 2]. Equivalently, F is divisorial if there is ...
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(4) mn = (xn) for all n ≥ 1. (5) Every nonzero ideal in A is equal to mn for some n ≥ 1. ... of K are: 0,K and. xnA for n ∈ Z. (These are called fractional ideals.) ...
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It is one-dimensional (i.e. it is not a field and every non-zero prime ideal of R is ... from other integral domains is that of the fractional ideal. From now on, ...
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for some nonzero a ∈ OK, we say I is a fractional ideal of OK. Further if aI is principal, we say I is principal. Denote the set of nonzero fractional ideals of OK by ...
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This necessitates the introduction of the following concept. 12.1.2. Definition. Let D be an integral domain with quotient field F. A fractional ideal of D is a nonzero ...
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