The Cartan-Brauer-Hua theorem for matrix and local matrix rings

The Cartan-brauer-hua Theorem for Matrix and Local Matrix Rings

A Generalization of the Cartan- Brauer-hua Theorem

2. G. Higman, On finite groups of exponent five, Proc. Cambridge Philos. Soc. 52 (1956), 381-390. 3. A. I. Kostrikin, On Burnside's problem, Dokl. Akad. Nauk SSSR 119 (1958), 1081-1084. (Russian) 4. M. Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. École Norm. Sup. (3) 71 (1954), 101-190. 5. H. Zassenhaus, Ein Verfahren, jeder endlichen p-Gruppe eine Lie-Ring mit der Charakteris...

Differential Polynomial Rings of Triangular Matrix Rings

MATRIX VALUATION PSEUDO RING (MVPR) AND AN EXTENSION THEOREM OF MATRIX VALUATION

Let R be a ring and V be a matrix valuation on R. It is shown that, there exists a correspondence between matrix valuations on R and some special subsets ?(MVPR) of the set of all square matrices over R, analogous to the correspondence between invariant valuation rings and abelian valuation functions on a division ring. Furthermore, based on Malcolmson’s localization, an alternative proof for t...

The Cartan Matrix of the Schur Algebra

ANNE E HENKE, UNIVERSIT AT KASSEL Abstra t. Let k be an in nite eld of prime hara teristi and let r be a positive integer. Using admissible de ompositions, we determine expli itly the entries of the de omposition matrix of the S hur algebra S(2; r) over k and prove that any two blo ks with the same number of simple modules have the the same de omposition matrix and hen e the same Cartan matrix...