Summary LetA→A′ be a regular morphism between two noetherian rings. Then for everyA-algebra of finite typeB, everyA-morphism fromB toA′ can be factorised through aB-algebra of finite typeB′ which is standard (smooth) overA and which is ?as smooth as possible? overB (i.e. except above the singular locus ofB overA). This result is a positive answer to one conjecture due to M. Artin.
Riassunto SiaA→A′ un omomorfismo regolare di anelli noetheriani. Si dimostra che per ogniA-algebraB di tipo finito, ogniA-omomorfismoB→A′ si può fattorizzare mediante unaB-algebraB′ di tipo finito che è liscia suA ed è ?la più liscia posibile? suB (più precisamente liscia suB meno il luogo singolare diB suA). Questo risultato è una risposta affermativa a una congettura di M. Artin.
A relative regular sequencea1, ...,ar, with respect to the idealI=(a1, ...,ar) has the property thatI annihilates the Koszul homology associated to each initial subsequence. This note analyzes the concepts of relative regular and proper sequences, two notions situated in a strategic position for studying the arithmetical properties of Blow-up Algebras in the largest context of generalized Cohen-Macaulay rings. 相似文献
Let (A, m) be an excellent Henselian ring with isolated singularity and letR be its completion. Then every indecomposable maximal Buchsbaum (resp. generalized Cohen-Macaulay)R-module is isomorphic with the completion of an indecomposable maximal Buchsbaum (resp. generalized Cohen-Macaulay)A-module. Hence one gets examples of non-complete, non-regular rings having finite Buchsbaum representation type. 相似文献
Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A~2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple. 相似文献
This paper deals with the study of compatibility between antihyperlipidemic agent atorvastatin calcium trihydrate (ATV) and eight pharmaceutical excipients used in the development of solid dosage forms, namely citric acid, anhydrous lactose, magnesium citrate, magnesium carbonate, sodium carboxymethyl cellulose, polyvinylpyrrolidone K30, colloidal silica and sorbitol. As investigational tools, universal attenuated total reflectance Fourier transform infrared spectroscopy and powder X-ray diffractogram patterns were used for binary mixtures of ATV with each excipient at ambient condition and then completed by subjecting the samples to thermal stress using thermal analysis (TG/DTG/HF), in non-isothermal conditions and in oxidative medium. It was shown the binary mixtures do not present interactions between ATV and excipients when stored under ambient conditions for 2 months, while under thermal stress, ATV presents interactions with sorbitol.
We provide irreducibility criteria for some classes of compositions of polynomials with integer coefficients of the form \(F\circ G\), with F being a quadratic irreducible polynomial and G a polynomial of arbitrary degree. 相似文献
We prove that, for positive integers a, b, c and d with c≠d, a>1, b>1, the number of simultaneous solutions in positive integers to ax2−cz2=1, by2−dz2=1 is at most two. This result is the best possible one. We prove a similar result for the system of equations x2−ay2=1, z2−bx2=1. 相似文献
We provide irreducibility criteria for multivariate polynomials with coefficients in an arbitrary field that extend a classical result of Pólya for polynomials with integer coefficients. In particular, we provide irreducibility conditions for polynomials of the form f(X)(Y ? f1(X))…(Y ? fn(X)) + g(X), with f, f1, ?, fn, g univariate polynomials over an arbitrary field. 相似文献