The fixed set of a derivation in lattices

被引：26
|
作者：
Xin, Xiao Long [1 ]
机构：
[1] NW Univ Xian, Dept Math, Xian 710069, Peoples R China
来源：
FIXED POINT THEORY AND APPLICATIONS | 2012年
关键词：
lattice; derivation; fixed set; ideal; standard ideal; RINGS;
D O I：
10.1186/1687-1812-2012-218
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The related properties of derivations in lattices are investigated. We show that the set of all isotone derivations in a distributive lattice can form a distributive lattice. Moreover, we introduce the fixed set of derivations in lattices and prove that the fixed set of a derivation is an ideal in lattices. Using the fixed sets of isotone derivations, we establish characterizations of a chain, a distributive lattice, a modular lattice and a relatively pseudo-complemented lattice, respectively. Furthermore, we discuss the relations among derivations, ideals and fixed sets in lattices.
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页数：12
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