منابع مشابه
The Theory of Numbers in Dedekind Rings
This paper explores some foundational results of algebraic number theory. We focus on Dedekind rings and unique factorization of prime ideals, as well as some celebrated consequences such as a partial proof of Fermat’s last theorem due to Kummer, and the law of quadratic reciprocity.
متن کاملϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES
The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...
متن کاملNotes on Dedekind Rings
These notes record the basic results about DVR’s (discrete valuation rings) and Dedekind rings, with at least sketches of the non-trivial proofs, none of which are hard. This is standard material that any educated mathematician with even a mild interest in number theory should know. It has often slipped through the cracks of Chicago’s first year graduate program, but then we would need at least...
متن کاملDedekind-finite Strongly Clean Rings
In this paper we partially answer two open questions concerning clean rings. First, we demonstrate that if a quasi-continuous module is strongly clean then it is Dedekind-finite. Second, we prove a partial converse. We also prove that all clean decompositions on submodules of continuous modules extend to the entire module.
متن کاملDedekind Domains and Rings of Quotients
We study the relation of the ideal class group of a Dedekind domain A to that of As, where S is a multiplicatively closed subset of A. We construct examples of (a) a Dedekind domain with no principal prime ideal and (b) a Dedekind domain which is not the integral closure of a principal ideal domain. We also obtain some qualitative information on the number of non-principal prime ideals in an ar...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1967
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(67)50062-8