点态化完备代数正规类中的Jacobson代数和Boolean代数
The Jacobson Algebras and Boolean Algebras in Normal Classes of Pointwise Complete Algebra
摘要: 定义了点态化完备代数正规类中的周期代数、Jacobson代数与Boolean代数，讨论了周期代数、Jacobson代数与Boolean代数的一些性质，证明了Jacobson代数类κ与Boolean代数类β都是遗传根类，但都不是超幂零根，从而都不是特殊根，并证明了正则根是遗传根，但不是超幂零根，从而不是特殊根。
Abstract: Periodic algebras, Jacobson algebras and Boolean algebras in normal classes of pointwise complete algebras are defined. Some properties of periodic algebras, Jacobson algebras and Boolean algebras are discussed. It is proved that both Jacobson algebra class κ and Boolean algebra class β are hereditary radicals, but they are not super nilpotent radicals, so they are not special radicals. It is also proved that regular radical is hereditary radical, but not super nilpotent radical, so it’s not a special radical.
文章引用：杨宗文, 何青海. 点态化完备代数正规类中的Jacobson代数和Boolean代数[J]. 理论数学, 2019, 9(9): 1009-1014. https://doi.org/10.12677/PM.2019.99127

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