Generating ideals in Prüfer domains
نویسندگان
چکیده
منابع مشابه
. A C ] 2 1 N ov 2 00 6 FACTORING IDEALS IN PRÜFER DOMAINS
We show that in certain Prüfer domains, each nonzero ideal I can be factored as I = I v Π, where I v is the divisorial closure of I and Π is a product of maximal ideals. This is always possible when the Prüfer domain is h-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the h-local property in Prüfer domains. We also explore ...
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The so-called Prüfer υ-multiplication domains PυMDs are usually defined as domains whose finitely generated nonzero ideals are t-invertible. These domains generalize Prüfer domains and Krull domains. The PυMDs are relatively obscure compared to their verywell-known special cases. One of the reasons could be that the study of PυMDs uses the jargon of star operations, such as the υ-operation and ...
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We present a randomized polynomial-time algorithm to generate a random integer according to the distribution of norms of ideals at most N in any given number field, along with the factorization of the integer. Using this algorithm, we can produce a random ideal in the ring of algebraic integers uniformly at random among ideals with norm up to N , in polynomial time. We also present a variant of...
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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,...
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Let ∗ be a star operation on an integral domain D. Let f(D) be the set of all nonzero finitely generated fractional ideals of D. Call D a ∗–Prüfer (respectively, (∗, v)–Prüfer) domain if (FF−1)∗ = D (respectively, (F vF−1)∗ = D) for all F ∈ f(D). We establish that ∗–Prüfer domains (and (∗, v)–Prüfer domains) for various star operations ∗ span a major portion of the known generalizations of Prüf...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1976
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1976.62.117