点态化完备代数正规类中的几乎幂零代数类
The Almost Nilpotent Classes in Normal Classes of Complete Pointwise Alagebras
摘要: 环及其它代数系统的根理论已经有了丰富的研究，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几乎幂零代数类α及其确定的下根性质L(α)，讨论了无非零几乎幂零理想代数类T={a∈A |a没有非0几乎幂零理想}确定的上根性质UT，证明了L(α) = UT。
Abstract: 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 almost nilpotent algebras α in the normal classes of pointwise complete algebras and the properties of the lower radical L(α) determined by α. We discuss the properties of the upper radical UT determined by the class T={a∈A |a has not nonzero almost ideals} of alge-bras without nonzero almost nilpotent ideals and prove that L(α) = UT.
文章引用：杨宗文, 娄本功. 点态化完备代数正规类中的几乎幂零代数类[J]. 理论数学, 2022, 12(9): 1527-1535. https://doi.org/10.12677/PM.2022.129166

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