| 原子根格中的大根环类 |
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| 引用本文： | 钟德强.原子根格中的大根环类[J].湖南工业大学学报,1995(4). |
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| 作者姓名： | 钟德强 |
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| 作者单位： | 株洲工学院基础课部 株洲412008 |
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| 摘 要： | 设W是全根格的子格。本文证明了:(1) 如果W是原子根格,则R∈W是W的大根环类当且仅当R包含W的所有原子;(2) 如果W是完备格且是原子格,则W中的所有大根环类的交是大根环类且是W的所有原子的并。作为特例给出了遗传根格、半遗传根格、次幂等根格中的大根环类的刻划,同时还给出了超幂零根格是否原子根格的一个判别条件。
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| 关 键 词： | 举环 *-环 根格 原子 大根 |
Large Radicals Classes in Atomic Lattices of Radicals |
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| Zhong Deqiang.Large Radicals Classes in Atomic Lattices of Radicals[J].Journal of Hnnnan University of Technology,1995(4). |
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| Authors: | Zhong Deqiang |
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| Abstract: | The article entitles Wa Sublattice of all radicals . and it proves that if W is an atomic lattice, then R is a large radical Classes in the W if and only if it contains all atoms of the W and vice versa. In the W ,the meet of all large radical Classes is the join of all atoms . As Corollaries, we give some Characteristics of the large members of lattices of hereditary. Semi-hereditary and Subidempotent radicals. In the paper,We also give an equiva-lent Condition When the lattice of supernilpotent radicals is an atomic lattice. |
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| Keywords: | Simple ring * -ring Lattice of radicals Atom Large radical class |
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