除环上方阵的Dieudonné行列式

DIEUDONNE DETERMINATS OF MATRICES OVER A DIVISION RING

本文给出除环上Dieudonné行列式的第二降阶定理、行列式展开定理等,并利用上述定理得到了强p除环上的正定自共轭阵行列式上界的新的估计。

This paper provides some new results on Dieudonn(?)an determinants over a di-vision ring, e. g., the 'second order-descending theorem', the 'spread theorem', andso on. As a concequence of these theorem, the upper bounds for Dieudonn(?)an deter-minants of positive definite conjugate quaternion matrices are given.