The lambda-dimension of commutative arithmetic rings

It is shown that every commutative arithmetic ring $R$ has $lambda$-dimension $leq 3$. An example of a commutative Kaplansky ring with $lambda$-dimension 3 is given. If $R$ satisfies an additional condition then $lambda$-dim($R$

Variation of the first Hilbert coefficients of parameters with a common integral closure

A problem posed by Wolmer V. Vasconcelos on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well

Deterministically Computing Reduction Numbers of Polynomial Ideals

We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I) variables. The second one computes via a Grobner system the set of all reduction numbers of the ideal I and thus in particular also its big reduction number. However,it requires computations in a ring with n.dim(I) parameters and n variables.Comment: This new version replaces the earlier version arXiv:1404.1721 and it has been accepted for publication in the proceedings of CASC 2014, Warsaw, Polna

The role of damped Alfven waves on magnetospheric accretion models of young stars

We examine the role of Alfven wave damping in heating the plasma in the magnetic funnels of magnetospheric accretion models of young stars. We study four different damping mechanisms of the Alfven waves: nonlinear, turbulent, viscous-resistive and collisional. Two different possible origins for the Alfven waves are discussed: 1) Alfven waves generated at the surface of the star by the shock produced by the infalling matter; and 2) Alfven waves generated locally in the funnel by the Kelvin-Helmholtz instability. We find that, in general, the damping lengths are smaller than the tube length. Since thermal conduction in the tube is not efficient, Alfven waves generated only at the star's surface cannot heat the tube to the temperatures necessary to fit the observations. Only for very low frequency Alfven waves ~10^{-5} the ion cyclotron frequency, is the viscous-resistive damping length greater than the tube length. In this case, the Alfven waves produced at the surface of the star are able to heat the whole tube. Otherwise, local production of Alfven waves is required to explain the observations. The turbulence level is calculated for different frequencies for optically thin and thick media. We find that turbulent velocities varies greatly for different damping mechanisms, reaching \~100 km s^{-1} for the collisional damping of small frequency waves.Comment: 29 pages, 12 figures, to appear in The Astrophysical Journa