منابع مشابه
Integrally Closed Modules and their Divisors
There is a beautiful theory of integral closure of ideals in regular local rings of dimension two, due to Zariski, several aspects of which were later extended to modules. Our goal is to study integral closures of modules over normal domains by attaching divisors/determinantal ideals to them. They will be of two kinds: the ordinary Fitting ideal and its divisor, and another ‘determinantal’ idea...
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Let (A, m) be an excellent normal local ring with algebraically closed residue class field. Given integrally closed m-primary ideals I ⊃ J , we show that there is a composition series between I and J , by integrally closed ideals only. Also we show that any given integrally closed m-primary ideal I, the family of integrally closed ideals J ⊂ I, lA(I/J) = 1 forms an algebraic variety with dimens...
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Let D be an integral domain with identity having quotient field K. This paper gives necessary and sufficient conditions on D in order that each integrally closed subring of O should belong to some subclass of the class of integrally closed domains ; some of the subclasses considered are the completely integrally closed domains, Prüfer domains, and Dedekind domains. 1. The class of integrally cl...
متن کاملIntegrally closed domains with monomial presentations
Let A be a finitely generated commutative algebra over a field K with a presentation A = K〈X1, . . . ,Xn | R〉, where R is a set of monomial relations in the generators X1, . . . ,Xn. Necessary and sufficient conditions are found for A to be an integrally closed domain provided that the presentation involves at most two relations. The class group of such algebras A is calculated. Examples are gi...
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ژورنال
عنوان ژورنال: Honam Mathematical Journal
سال: 2011
ISSN: 1225-293X
DOI: 10.5831/hmj.2011.33.3.425