The fixed set of a derivation in lattices

Fixexd point theory and applications

Xiao Long Xin¹ 

[1] Department of Mathematics, Northwest University, Xi’an, P.R. China

关键词: lattice;    derivation;    fixed set;    ideal;    standard ideal;   

DOI  :  10.1186/1687-1812-2012-218

学科分类：数学（综合）

来源: SpringerOpen

【 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. MSC:06B35, 06B99.

【 授权许可】

CC BY