点态化完备代数正规类中的绝对半素代数类与绝对素代数类

The Absolutely Semiprime Algebras Class and the Absolutely Prime Algebras Class in Normal Classes of Complete Pointwise Algebras

环及其它代数系统的根理论有了丰富的研究,Puczylowski建立了一般代数正规类的根理论。本文研究点态化完备代数正规类中的绝对半素代数类τs与绝对素代数类τ及其确定的上根性质Uτs,Uτ,证明了Uτs是超幂零根,Uτ是特殊根,τs是遗传根。

The radicals of rings and other various algebraic structures have been researched very much. Puczylowski established the general theory of radicals of the objects called algebras. In this paper, we study the absolutely semiprime algebras class τs and the absolutely semiprime algebras class τ in the normal classes of pointwise complete algebras and the properties of the upper radical Uτs, Uτ determined by τs and τ, it is proved that Uτs is a supernilpotent radical, Uτ is a special radical and τs is a hereditary radical.