n环R(n)的模刻划和同态基本定理

THE CHARACTER OF N-RING R(n) BY MODULES AND ITS FUNDEMANTAL HOMOMORPHISM THEOREM

在[1]文中深入研究了m群,[2]文中定义了n环和R(n)-M_m^1范畴,本文继续研究n环,给出了n环的同态基本定理,(§1),证明了交换m群为n环R(n)上模当且仅当存在从R(n)到End的一个(n,m)环同态,最后利用循环模类刻划n除环。

In this paper, we give the Fundemantal Homomorphism Theorem of n-rings of the first class, then we prove that a abelian m-group M is a R(n)-module if and onty if there is a (n, m) ring homomorphism from R(n) to EndM, at Iast we characterise a m division ring with a cyclic module.