منابع مشابه
Dedekind 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...
متن کاملA NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS
In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...
متن کاملMath 254a: Rings of Integers and Dedekind Domains
Proof. Let (α1, . . . , αn) be any Q-basis for K; we first claim there for each i, there exists a non-zero di ∈ Z such that diαi ∈ OK . Indeed, it is easy to check that it is enough to let di be the leading term of any integer polynomial satisfied by αi. Thus, for any non-zero β ∈ I, we find that (βd1α1, . . . , βdnαn) is a Q-basis for K contained in I. It remains to show that such a basis with...
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...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1965
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1965.15.59