CHARACTERIZATIONS OF DISTRIBUTIVE LATTICES AND SEMICONTINUOUS LATTICES
CHARACTERIZATIONS OF DISTRIBUTIVE LATTICES AND SEMICONTINUOUS LATTICES
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分布格子和半连续格子的特征
DOI：
10.4134/bkms.2010.47.3.633
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发表时间：
2010-05-01
影响因子：
0.5
通讯作者：
Shi Weixue
中科院分区：
文献类型：
--
作者：
Jiang Guanghao;Shi Weixue
本文引入并研究了偏序集上关于滤子的极大理想的概念。给出了分配格的一个内在刻画。此外，我们还给出了非连续格中伪素数的一个刻划和非连续格的一个刻划。研究了保序且非连续格的函数。引入并研究了半算术格的一个新概念。
In this paper, the concept of maximal ideals relative to a fil- ter on posets is introduced and examined. An intrinsic characterization of distributive lattices is obtained. In addition, we also give a characteri- zation of pseudo primes in semicontinuous lattices and a characterization of semicontinuous lattices. Functions of semicontinuous lattices which are order preserving and semicontinuous are studied. A new concept of semiarithmetic lattices is introduced and examined.