点态化完备代数正规类中的低幂等根  

The Hypoidempotent Radicals in Normal Classes of Pointwise Complete Alagebra

作　　者：杨宗文[1] 娄本功[1] 

机构地区：[1]云南大学数学系,云南 昆明

出　　处：《理论数学》2021年第1期1-6,共6页Pure Mathematics

摘　　要：定义了点态化完备代数正规类中的低幂等根,证明了Boolean根β、正则根ν、遗传幂等根χ、λ-根λ、幂等代数根ι都是低幂等根,并且这5个低幂等根满足β≤ν≤χ≤λ≤ι。进一步,证明了低幂等根半单类包含所有0乘代数,幂等代数根ι半单类满足弱同态闭性质。The hypoidempotent radicals in normal classes of pointwise complete algebras are defined. It is proved that the Boolean radical β, regular radical ν, hereditary idempotent radical χ, λ-radical λ and idempotent algebras radical ι are all hypoidempotent radicals, and these five hypoidempotent radicals satisfy β≤ν≤χ≤λ≤ι. Furthermore, it is proved that the semisimple class of hypoidempotent radicals contains all 0-multiplication algebras, and the semisimple classes of idempotent algebras radical ι is the weakly homomorphically closed.

关 键 词：点态化完备代数正规类 幂等代数根ι β-根β 遗传幂等代数根χ λ-根λ 正则根ν 低幂等根 

分 类 号：O15[理学—数学]