ﻻ يوجد ملخص باللغة العربية
The Qth-power algorithm produces a useful canonical P-module presentation for the integral closures of certain integral extensions of $P:=mathbf{F}[x_n,...,x_1]$, a polyonomial ring over the finite field $mathbf{F}:=mathbf{Z}_q$ of $q$ elements. Here it is shown how to use this for several small primes $q$ to reconstruct similar integral closures over the rationals $mathbf{Q}$ using the Chinese remainder theorem to piece together presentations in different positive characteristics, and the extended Euclidean algorithm to reconstruct rational fractions to lift these to presentations over $mathbf{Q}$.
For a pair $(R, I)$, where $R$ is a standard graded domain of dimension $d$ over an algebraically closed field of characteristic $0$ and $I$ is a graded ideal of finite colength, we prove that the existence of $lim_{pto infty}e_{HK}(R_p, I_p)$ is equ
The main aim of this article is to study the relation between $F$-injective singularity and the Frobenius closure of parameter ideals in Noetherian rings of positive characteristic. The paper consists of the following themes, including many other top
We classify plethories over fields of characteristic zero, thus answering a question of Borger-Wieland and Bergman-Hausknecht. All plethories over characteristic zero fields are linear, in the sense that they are free plethories on a bialgebra. For t
We give a version of the usual Jacobian characterization of the defining ideal of the singular locus in the equal characteristic case: the new theorem is valid for essentially affine algebras over a complete local algebra over a mixed characteristic
Let k be a perfect field of positive characteristic, k(t)_{per} the perfect closure of k(t) and A=k[[X_1,...,X_n]]. We show that for any maximal ideal N of A=k(t)_{per}otimes_k A, the elements in hat{A_N} which are annihilated by the Taylor Hasse-Sch