Let R be a Noetherian ring . We prove that has global dimension at most two if, and only every prime ideal of is linear type. Similarly, we show three syzygetic. As consequence, derive characterization these rings using the André-Quillen homology.

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integer n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd prime p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some progr...

The bas ic principles of the group properti es of physical quantities are reviewed. The proble ms assoc iated with th e dimensions of angle and logarithm are solved by using functional equations, ins tead of a nalytic express ions , for de fining functions of non numerical quantities. It is concluded that the neper and radian are related by Np= j rad , so that when the radian is considered as a...

Abstract. We define a classical probability analog of Voiculescu’s free entropy dimension that we shall call the classical probability entropy dimension. We show that the classical probability entropy dimension is related with diverse other notions of dimension. First, it equals the fractal dimension. Second, if one extends Bochner’s inequalities to a measure by requiring that microstates aroun...

We describe a computer intensive method for linear dimension re duction which minimizes the classi cation error directly Simulated annealing Bohachevsky et al is used to solve this problem The classi cation error is determined by an exact integration We avoid distance or scatter measures which are only surrogates to circumvent the classi cation error Simulations in two dimensions and analytical...

We investigate the reverse mathematics of several theorems about partial orders. We mainly focus on the analysis of scattered (no copy of the rationals) and FAC (no infinite antichains) partial orders, for which we consider many characterization theorems (for instance the wellknown Hausdorff’s theorem for scattered linear orders). We settle the proof-theoretic strength of most of these theorems...

This paper characterizes the first cohomology group H(G,M) where M is a Banach space (with norm || ||M) that is also a left CG module such that the elements of G act on M as continuous C-linear transformations. We study this group for G an infinite, finitely generated group. Of particular interest are the implications of the vanishing of the group H(G,M). The first result is that H(G,CG) imbeds...