Relation between ideal numbers and ideals of a ring?

Asked May 18 '15 at 10:25

Active May 18 '15 at 10:45

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I would like to know whether the ideal numbers of Kummer (or the ideals of Dedekind for that matter) are closely related to the concept of ideal (right ideal, left ideal, two-sided ideal and so on.....) in a ring. If so, in which manner? Or are they eventually the same thing?

Thanks in advance

edited May 18 '15 at 10:45

asked May 18 '15 at 10:25

Javier Arias

2,033

Could you provide some reference or definition for these concepts? – Tobias Kildetoft May 18 '15 at 10:27
you find a reference, for instance, in Kolmogorov's encyclopaedia – Javier Arias May 18 '15 at 10:30
Do you have a reference that one can easily find? – Tobias Kildetoft May 18 '15 at 10:33
http://en.wikipedia.org/wiki/Ideal_%28ring_theory%29 – Javier Arias May 18 '15 at 10:49
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Does this answer shed light? – Daniel Fischer May 18 '15 at 10:53
@Daniel Fischer.It does shed light with regard to the specifics of Kummer's invention and Dedekind's development thereafter. However, what I want to know is the relation between that and the definition of Ideal, Right-Ideal and so on in Ring Theory as it is known today. It wold also be nice to know who set that relation as well...... – Javier Arias May 18 '15 at 10:58

Relation between ideal numbers and ideals of a ring?

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