Über algebraische Relationen zwischen additiven und multiplikativen Funktionen.
Über Basen nulldimensionaler Polynomideale
Über den regulären Ort in ausgezeichneten Ringen.
Über die Distributivität des Idealverbandes eines kommutativen Ringes.
Über die Gleichheit von absoluter und realtiver Lipschitz-Saturation bei analytischen Algebren.
Über halbprimäre ideale und halbprimäre Ringe
Ultrafiltres sur un espace spectral - Anneaux de Baer - Anneaux a spectre minimal compact.
Un anneau de Prüfer
Let be the ring of integer valued polynomials over . This ring is known to be a Prüfer domain. But it seems there does not exist an algorithm for inverting a nonzero finitely generated ideal of . In this note we show how to obtain such an algorithm by deciphering a classical abstract proof that uses localisations of at all prime ideals of . This confirms a general program of deciphering abstract classical proofs in order to obtain algorithmic proofs.
Uniform bounds in noetherian rings.
Uppers to zero in and almost principal ideals
Let be an integral domain with quotient field and a polynomial of positive degree in . In this paper we develop a method for studying almost principal uppers to zero ideals. More precisely, we prove that uppers to zero divisorial ideals of the form are almost principal in the following two cases: – , the ideal generated by the leading coefficients of , satisfies . – as the -submodule of is of finite type. Furthermore we prove that for we have: – . – If there exists , then ...
Valuation ideals with zero divisors.
Valuation Near-Rings.
Valuations and lengths of constructible modules.
Valuations des anneaux et des corps non commutatifs
v-closed ideal and Prüfer rings.
When spectra of lattices of -ideals are Stone-Čech compactifications
Let be a completely regular Hausdorff space and, as usual, let denote the ring of real-valued continuous functions on . The lattice of -ideals of has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) precisely when is a -space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a -ideal if whenever two elements have the same annihilator and...
When the Dual of an Ideal is a Ring.
Young Diagrams and Determinantal Varieties.
z⁰-Ideals and some special commutative rings
In a commutative ring R, an ideal I consisting entirely of zero divisors is called a torsion ideal, and an ideal is called a z⁰-ideal if I is torsion and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We prove that in large classes of rings, say R, the following results hold: every z-ideal is a z⁰-ideal if and only if every element of R is either a zero divisor or a unit, if and only if every maximal ideal in R (in general, every prime z-ideal) is a z⁰-ideal,...
Zero Estimates on Group Varieties I.