منابع مشابه
Prime Ideals and Integral Dependence
Let 9t and © be commutative rings such that © contains, and has the same identity element as, 9Î. If p and $ are prime ideals in SK and © respectively such that ^P\9t = p then we shall say that $ lies over, or contracts to, p. If over every prime ideal in dt there lies a prime ideal in ©, we shall say that the "lying-over" theorem holds for the pair of rings 9Î and ©. Suppose now that q and p a...
متن کاملDepths of Multiplier Ideals and Integral Closure
In this note, we study how the depths of multiplier ideals behave under restriction. We also study possible values of the depths of multiplier ideals in the filtrations induced from maximal ideal sheaves. We then use it to give a sufficient condition for the integral closedness of the product of a multiplier ideal and a power of maximal ideal sheaf in the spirit of Huneke.
متن کاملIntegral and ideals in Riesz spaces
A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. A.M.S. SUBJECT CLASSIFICATION (2000): 28B15.
متن کاملToric Ideals of Integral Closures from Graphs
A graph-theoretic method, simpler than existing ones, is used to characterize the minimal set of monomial generators for the integral closure of any polynomial ring generated by quadratic monomials. The toric ideal of relations between these generators is generated by a set of graphically described binomials. The spectra of the original ring and of its integral closure turn out to be canonicall...
متن کاملDerivations and the Integral Closure of Ideals
Let (R, m) be a complete local domain containing the rationals. Then there exists an integer l such that for any ideal I ⊆ R, if f ∈ m, f / ∈ In, then there exists a derivation δ of R with δ(f) / ∈ In+l. This note grew out of a question raised by C. Huneke some years ago: Suppose (R, m) is a complete local domain with perfect residue class field k which it contains. Call an element x ∈ R deriva...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1981
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500004638