Using a class sum and a collection of related Radon transforms, we present a proof G. James’s Kernel Intersection Theorem for the complex unipotent representations of the finite general linear groups. The approach is analogous to that used by F. Scarabotti for a proof of James’s Kernel Intersection Theorem for the symmetric group. In the process, we also show that a single class sum may be used...

A keystone in the classical theory of diophantine approximation is the construction of an auxilliary polynomial. The polynomial is constructed so that it is forced (for arithmetic reasons) to vanish at certain approximating points and this contradicts an upper bound on the order of vanishing obtained by other (usually geometric) techniques; the contradiction then allows one to prove finiteness ...

In this paper we study some results on Noetherian semigroups. We  show that if  $S_S$ is an  strongly  faithful $S$-act and $S$ is a duo weakly Noetherian, then we have the following.

An additive category in which each object has a Krull-Remak-Schmidt decomposition—that is, finite direct sum decomposition consisting of objects with local endomorphism rings—is known as Krull-Schmidt category. A Hom-finite is an for there commutative unital ring k, such that Hom-set length k-module. The aim this note to provide proof Krull-Schmidt, if and only it split idempotents, indecomposa...

The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

Erdos and Rado defined a A-system, as a family in which every two members have the same intersection. Here we obtain a new upper bound on the maximum cardinality q ( n , q ) of an n-uniform family not containing any A-system of cardinality q. Namely, we prove that, for any a > 1 and q , there exists C = C(a, q ) such that, for any n ,

This paper determines when the Krull-Schmidt property holds for all finitely generated modules and for maximal Cohen-Macaulay modules over one-dimensional local rings with finite Cohen-Macaulay type. We classify all maximal CohenMacaulay modules over these rings, beginning with the complete rings where the Krull-Schmidt property is known to hold. We are then able to determine when the Krull-Sch...

The concepts of tropical semiring and tropical hypersurface, are extended to the case of an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator “tropicalization” we conclude with an extension of Kapranov’s theorem to algebraically closed fields together with a valuation over...

1 Introduction